Tvardi Therapeutics, Inc.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act of 1934

(Amendment No.__)

Filed by the Registrant☒

Filed by a party other than the Registrant☐

Check the appropriate box:

TVARDI THERAPEUTICS, INC.

(Name of Registrant as Specified in Its Charter)

(Name of Person(s) Filing Proxy Statement if other than the Registrant)

Payment of Filing Fee (Check all boxes that apply):

TVARDI THERAPEUTICS, INC.

3 Sugar Creek Ctr. Blvd.

Suite 525

Sugar Land, Texas 77478

NOTICE OF ANNUAL MEETING OF STOCKHOLDERS

To Be Held on June 9, 2026

Dear Stockholder:

You are cordially invited to attend the 2026 Annual Meeting of Stockholders of Tvardi Therapeutics, Inc., a Delaware corporation (“Tvardi,” “we,” “us,” “our” or the “Company”). The meeting will be held virtually, via live webcast atwww.virtualshareholdermeeting.com/TVRD2026, at 12:00 p.m., Eastern Daylight Time on Tuesday, June 9, 2026 for the following purposes:

These items of business are more fully described in the proxy statement accompanying this Notice of Annual Meeting of Stockholders.

The record date for the Annual Meeting is Tuesday, April 14, 2026. Only stockholders of record at the close of business on that date may vote at the meeting or any adjournment thereof.

Important Notice Regarding the Availability of Proxy Materials for the Stockholders’ Meeting to Be Held Virtually, Via Live Webcast at www.virtualshareholdermeeting.com/TVRD2026, at 12:00 p.m., Eastern Daylight Time on Tuesday, June 9, 2026.The proxy statement and the annual report to stockholders are available at www.proxyvote.com.

You are cordially invited to attend the meeting online. Whether or not you expect to attend the meeting, please vote over the telephone or the internet as instructed in these materials, or, if you receive a paper proxy card by mail, by completing and returning the proxy mailed to you, as promptly as possible in order to ensure your representation at the meeting.Even if you have voted by proxy, you may still vote online if you attend the Annual Meeting. Please note, however, that if your shares are held of record by a broker, bank or other agent and you wish to vote at the Annual Meeting, you must follow the instructions from such organization and will need to obtain a proxy issued in your name from that record holder.

EXPLANATORY NOTE

On April 15, 2025 (the “Closing Date”), the Delaware corporation formerly known as “Cara Therapeutics, Inc.” completed its previously announced merger with Tvardi Therapeutics, Inc. (“Legacy Tvardi”) in accordance with the terms of 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 (“Merger Sub”), and Legacy Tvardi, pursuant to which Merger Sub merged with and into Legacy Tvardi, with Legacy Tvardi surviving the merger as a wholly owned subsidiary of Cara (the “Merger”). Also on April 15, 2025, Cara changed its name from “Cara Therapeutics, Inc.” to “Tvardi Therapeutics, Inc.” (“Tvardi,” the “Company,” “we,” “our,” or “us”).

Pursuant to the Merger Agreement, on the Closing Date, (i) Cara effected a 1-for-3 reverse stock split of its common stock (the “Reverse Stock Split”), (ii) Cara increased its authorized shares of common stock to 150,000,000, (iii) Merger Sub was merged with and into Legacy Tvardi and Legacy Tvardi became a wholly owned subsidiary of the Company, and (iv) the Company changed its name to “Tvardi Therapeutics, Inc.” Following the completion of the Merger, the business conducted by the Company became primarily the business conducted by Legacy Tvardi, which is a clinical-stage biopharmaceutical company focused on the development of novel, oral small molecule therapies targeting STAT3 to treat fibrosis-driven diseases with significant unmet need.

Immediately prior to the effective time of the Merger, each share of Legacy Tvardi’s preferred stock was converted into one share of Legacy Tvardi’s common stock. At the effective time of the Merger, the Company issued an aggregate of 7,805,161 shares of its common stock to Legacy Tvardi’s stockholders and holders of outstanding convertible promissory notes (the “Convertible Notes”) of Legacy Tvardi, based on (i) an exchange ratio calculated in accordance with the Merger Agreement (the “Exchange Ratio”) and (ii) the terms of the Convertible Notes, resulting in 9,355,542 shares of the Company’s common stock being issued and outstanding immediately following the effective time of the Merger.

As of the open of trading on April 16, 2025, the common stock of the Company began trading on The Nasdaq Capital Market (“Nasdaq”) under the symbol “TVRD.”