SEC Form 424B3 filed by Tvardi Therapeutics Inc.

2,084,117 Shares of Common Stock

This prospectus supplement supplements the prospectus dated November 8, 2025 (the “Prospectus”), which forms a part of our registration statement on Form S-1 (No. 333-287675). This prospectus supplement is being filed to update and supplement the information in the Prospectus with certain information contained in our Current Reports on Form 8-K, filed with the Securities and Exchange Commission on December 18, 2025 and March 6, 2026 (collectively, the “Current Reports”). Accordingly, we have attached the Current Reports in relevant part to this prospectus supplement.

The Prospectus and this prospectus supplement relates to the resale by certain of the selling stockholders named in the Prospectus (each a “selling stockholder” and, collectively, the “selling stockholders”) of up to 2,084,117 shares of our common stock, par value $0.001 per share (“common stock”) issued to the selling stockholders pursuant to the Agreement and Plan of Merger and Reorganization, dated as of December 17, 2024 (the “Merger Agreement”), by and among Cara Therapeutics, Inc. (“Cara”), CT Convergence Merger Sub, Inc., a wholly owned subsidiary of Cara, and Tvardi Therapeutics, Inc.

Our common stock is listed on The Nasdaq Capital Market (“Nasdaq”) under the symbol “TVRD.” On March 5, 2026, the last quoted sale price for our common stock as reported on Nasdaq was $4.02.

This prospectus supplement should be read in conjunction with the Prospectus, including any amendments or supplements thereto, which is to be delivered with this prospectus supplement. This prospectus supplement is qualified by reference to the Prospectus, including any amendments or supplements thereto, except to the extent that the information in this prospectus supplement updates and supersedes the information contained therein.

This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus, including any amendments or supplements thereto.

Investing in our securities involves a high degree of risk. Before buying any securities, you should carefully read the discussion of the risks of investing in our securities in the section titled “Risk Factors” beginning on page 5 of the Prospectus and under similar headings in any amendments or supplements to the Prospectus.

Neither the Securities Exchange Commission nor any state securities commission has approved or disapproved of these securities or determined if this prospectus is truthful or complete. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is March 6, 2026.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 OR 15(d) of The Securities Exchange Act of 1934

Date of Report (Date of earliest event reported) December 16, 2025

TVARDI THERAPEUTICS, INC.

(Exact name of registrant as specified in its charter)

Registrant's telephone number, including area code: (713) 489-8654

Not Applicable

(Former Name or Former Address, if Changed Since Last Report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instruction A.2.):

Securities registered pursuant to Section 12(b) of the Act:

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§240.12b-2 of this chapter).

Emerging growth company ¨

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ¨

Item 5.02. Departure of Directors or Certain Officers, Election of Directors, Appointment of Certain Officers; Compensatory Arrangements of Certain Officers.

Retention Compensation

On December 16, 2025, the Board of Directors of Tvardi Therapeutics, Inc. (the “Company”) approved one-time retention compensation for certain of the Company’s employees, as recommended by the Compensation Committee of the Board, including to each of the Company’s named executive officers, as follows:

The Board approved the retention compensation to further incentivize the named executive officers’ performance as the Company executes on its Phase 1b/2 clinical trial of TTI-101 in hepatocellular carcinoma and Phase 1 trial of TTI-109 in healthy volunteers.

Tvardi Therapeutics, Inc. Severance and Change in Control Plan

On December 16, 2025, the Board approved the Tvardi Therapeutics, Inc. Severance and Change in Control Plan (the “Severance Plan”), as recommended by the Compensation Committee of the Board.

The purpose of the Severance Plan is to provide for the provision of certain severance and equity vesting acceleration benefits to certain employees of the Company (collectively, the “Eligible Employees”), including without limitation all of the Company’s existing named executive officers. As a condition for eligibility, participants must enter into a participation agreement, which specifies the potential severance benefits and contains other terms and conditions related to participation in the Severance Plan. The severance benefits are payable upon a qualifying termination of employment (a “Covered Termination”), both before and after a Change in Control of the Company (as defined in the Severance Plan). A Covered Termination is defined as a termination without Cause (other than as a result of death or disability) or, with respect to Imran Alibhai, Dan Conn and John Kauh, a resignation for Good Reason (each as defined in the Severance Plan or applicable participation agreement).

Except as otherwise provided in a participation agreement, the Severance Plan supersedes any change in control or severance benefit plan, policy or practice previously maintained by the Company with respect to an Eligible Employee and any change in control or severance benefits in any individually negotiated employment offer letter, contract or other agreement between the Company and an Eligible Employee. Notwithstanding the foregoing, the Eligible Employee’s outstanding equity awards remain subject to the terms of the equity plan under which such awards were granted (including the relevant award documentation) that may apply upon a Change in Control and/or termination of such Eligible Employee’s service.

Each Eligible Employee’s right to receive the payments and benefits provided under the Severance Plan are subject to such Eligible Employee’s execution of a general waiver and release, in such form as provided by the Company. An Eligible Employee’s right to receive benefits under the Severance Plan shall terminate under certain circumstances, as specified in the Severance Plan.

Severance Benefits of Eligible Employees Within Change in Control Period

If an Eligible Employee is terminated in a Covered Termination commencing three months prior to and ending 12 months following the closing of a Change in Control (the “Change in Control Period”), such Eligible Employee will be eligible to receive the following benefits, subject to standard deductions and withholdings: (i) a lump sum cash payment equal to a portion of such Eligible Employee’s base salary (18 months for Dr. Alibhai, 12 months for Mr. Conn and Dr. Kauh); (ii) a lump sum cash payment in an amount equal to 150% (for Dr. Alibhai) or 100% (for Mr. Conn and Dr. Kauh) of the Eligible Employee’s annual target cash bonus for the calendar year in which the Eligible Employee’s Covered Termination occurs; (iii) Company-paid COBRA premium payments for the Eligible Employee and such Eligible Employee’s eligible dependents for a period of time following such Covered Termination (up to 18 months for Dr. Alibhai, 12 months for Mr. Conn and Dr. Kauh); (iv) full acceleration of any then-outstanding, unvested time-vesting equity awards held by the Eligible Employee and (v) with respect to Mr. Conn, a lump sum cash payment in lieu of any unused portion of his accrued vacation (“PTO”).  If any of the benefits payable under the Severance Plan would constitute a “parachute payment” within the meaning of Section 280G of the Code (as defined in the Severance Plan) and otherwise be subject to the excise tax imposed by Section 4999 of the Code, the Severance Plan provides for a best-after-tax analysis with respect to such payments.

Severance Benefits of Eligible Employees Outside Change in Control Period

If an Eligible Employee is terminated in a Covered Termination outside of the Change in Control Period, such Eligible Employee will be eligible to receive: (i) continued cash payments of such Eligible Employee’s base salary, to be paid in installments in accordance with the Company’s regular payroll practices over a specified time period (12 months for Dr. Alibhai, 10 months for Mr. Conn and 9 months for Dr. Kauh); (ii) for the named executive officers, a pro-rated amount of the officer’s annual target cash bonus based upon (a) actual performance as measured by the Plan Administrator (as defined in the Severance Plan) and (b) the number of months worked in the calendar year in which such officer’s Covered Termination occurs; (iii) Company-paid COBRA premiums for the Eligible Employee and such Eligible Employee’s eligible dependents for a period of time (up to 12 months for Dr. Alibhai, 10 months for Mr. Conn and 9 months for Dr. Kauh); (iv) acceleration of the vesting and exercisability (as applicable) of any then-outstanding, unvested time-vesting equity awards held by the named executive officers to the extent such awards were scheduled to vest during a specified period following such Covered Termination (24 months for Dr. Alibhai, 10 months for Mr. Conn or 9 months for Dr. Kauh) and (v) with respect to Mr. Conn, PTO.

Change in Control Acceleration upon Acquirer’s Failure to Assume, Continue or Substitute

If (i) in connection with a Change in Control, any outstanding unvested equity award held by an Eligible Employee is not assumed, continued or substituted for by the successor or acquiror entity (or its parent company) and (ii) such Eligible Employee remains employed with the Company as of immediately prior to such Change in Control, then the vesting of such awards shall accelerate in full (and, with respect to performance-vesting awards, at 100% of target, unless otherwise provided in individual award documents), effective immediately prior to, but subject to the consummation of, such Change in Control.

* * *

The foregoing description of the Severance Plan is only a summary and is qualified in its entirety by reference to the full text of the Severance Plan, a copy of which will be filed with the Company’s Annual Report on Form 10-K for the year ended December 31, 2025.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, as amended, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of
The Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): March 6, 2026

Tvardi Therapeutics, Inc.

(Exact name of Registrant as specified in its charter)

(713) 489-8654

(Registrant's telephone number, including area code)

Not Applicable

(Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instruction A.2. below):

Securities registered pursuant to Section 12(b) of the Act:

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§240.12b-2 of this chapter).

Emerging growth company ¨

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ¨

Tvardi Therapeutics, Inc. (the “Company”) has set June 9, 2026 as the date for the Company’s 2026 Annual Meeting of Stockholders (the “2026 Annual Meeting”). Proposals of stockholders intended to be presented at the 2026 Annual Meeting pursuant to Rule 14a-8 promulgated under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), must be received by the Company at its principal executive offices a reasonable time before the Company begins to print and send its proxy materials in order to be considered for inclusion in the Company’s proxy statement and proxy card relating to the 2026 Annual Meeting. The Company will consider proposals received on or before March 16, 2026 to have been received a reasonable time before the Company begins to print and send its proxy materials.

In addition, the Company’s Amended and Restated Bylaws (the “Bylaws”) establish an advance notice procedure for nominations for election to the Board of Directors of the Company (the “Board”) and other matters that stockholders wish to present for action at an annual meeting other than those to be included in the Company’s proxy statement. The Company must receive such proposals by the later of the close of business on the 90th day prior to such annual meeting and the 10th day following the day on which public announcement of the date of such meeting was first made. For the 2026 Annual Meeting, such deadline falls on March 16, 2026. If the stockholder fails to give notice by this date, then the persons named as proxies in the proxies solicited by the Board for the 2026 Annual Meeting may exercise discretionary voting power regarding any such proposal. The Bylaws specify requirements as to the form and content of a stockholder’s notice.

In addition to satisfying the advance notice provisions in the Bylaws relating to director nominations, including the earlier notice deadlines set out above, to comply with Rule 14a-19, the Securities and Exchange Commission’s universal proxy rule, stockholders who intend to solicit proxies in support of director nominees other than the Company’s nominees in compliance with Rule 14a-19 under the Exchange Act must also provide notice that sets forth the information required by Rule 14a-19 by the later of 60 days prior to the date of the annual meeting or the 10th day following public announcement by the Company of the date of the annual meeting. For the 2026 Annual Meeting, such deadline falls on April 10, 2026.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the Registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.