EX-99.(a)(1)(iv)

Exhibit (a)(1)(iv)

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

TERNS PHARMACEUTICALS, INC.

$53.00 Net per Share of Common Stock

Pursuant to the Offer to Purchase Dated April 7, 2026

THAILAND MERGER SUB, INC.

a wholly owned subsidiary of

MERCK SHARP & DOHME LLC

a wholly owned subsidiary of

MERCK & CO., INC.

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE ONE MINUTE FOLLOWING 11:59 P.M., EASTERN TIME, ON MAY 4, 2026, UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED.

To Our Clients:

Enclosed for your consideration are the Offer to Purchase dated April 7, 2026 (the “Offer to Purchase”), the related Letter of Transmittal (as it may be amended or supplemented from time to time, the “Letter of Transmittal” and, together with the Offer to Purchase, the “Offer”) in connection with the offer by Thailand Merger Sub, Inc., a Delaware corporation (“Purchaser”) and a wholly owned subsidiary of Merck Sharp & Dohme LLC, a New Jersey limited liability company (“Parent”), to acquire all of the outstanding shares of common stock, par value $0.0001 per share (the “Shares”), of Terns Pharmaceuticals, Inc., a Delaware corporation (“Terns”), for $53.00 per Share (the “Offer Price”) in cash, without interest, subject to any applicable withholding of taxes, upon the terms and subject to the conditions set forth in the Offer. Also enclosed is Terns’ Tender Offer Solicitation/Recommendation Statement on Schedule 14D-9.

We or our nominees are the holder of record of Shares held for your account. A tender of such Shares can be made only by us or our nominees as the holder of record and pursuant to your instructions. The enclosed Letter of Transmittal is furnished to you for your information only and cannot be used by you to tender Shares held by us or our nominees for your account.

We request instructions as to whether you wish us to tender any or all of the Shares held by us or our nominees for your account, upon the terms and subject to the conditions set forth in the Offer.

Your attention is directed to the following:

The Offer Price is $53.00 per Share, in cash, without interest, subject to any applicable withholding of taxes, upon the terms and subject to the conditions set forth in the Offer.

The Offer is being made for all outstanding Shares.

The Offer is being made pursuant to the Agreement and Plan of Merger, dated as of March 24, 2026 (together with any amendments or supplements thereto, the “Merger Agreement”), among Terns, Parent and Purchaser. The Merger Agreement provides, among other things, that as soon as reasonably practicable following (but in any event within one business day of) the acceptance of the Shares for

payment (the “Offer Acceptance Time”), subject to the satisfaction or waiver of the conditions set forth in the Merger Agreement, and in accordance with the relevant provisions of the Delaware General Corporation Law (the “DGCL”) and other applicable legal requirements, Purchaser will merge with and into Terns (the “Merger” and, together with the Offer and the other transactions contemplated by the Merger Agreement, the “Transactions”), with Terns continuing as the surviving corporation and a wholly owned indirect subsidiary of Parent. At the effective time of the Merger (being such date and at such time as the certificate of merger in respect of the Merger is duly filed with the Secretary of State of the State of Delaware or at such later time and date as may be agreed upon by the parties to the Merger Agreement in writing and specified in the certificate of merger in accordance with the DGCL, the “Effective Time”), each outstanding Share (other than (i) Shares held by Terns (or held in Terns’ treasury), Parent, Purchaser, or any other direct or indirect wholly owned subsidiary of Terns, Parent or Purchaser, (ii) Shares irrevocably accepted for purchase in the Offer and (iii) Shares issued and outstanding immediately prior to the Effective Time that are held by holders who are entitled to appraisal rights under Section 262 of the DGCL and have properly exercised and perfected their respective demands for appraisal of such Shares in the time and manner provided in Section 262 of the DGCL and, as of the Effective Time, have neither validly withdrawn nor lost their rights to such appraisal and payment under the DGCL) will be automatically converted into the right to receive the Offer Price, in cash, without interest, subject to any applicable withholding of taxes. No appraisal rights are available in connection with the Offer. However, if the Offer is successful and the Merger is consummated, any Shares issued and outstanding as of immediately prior to the Effective Time which are held of record or beneficially owned by holders who (A) did not tender their Shares in the Offer (or, if tendered, validly and subsequently withdrew such Shares prior to the Offer Acceptance Time); (B) follow the procedures set forth in Section 262 of the DGCL; (C) do not thereafter withdraw their demand for appraisal of such Shares or otherwise lose their appraisal rights, in each case in accordance with Section 262 of the DGCL; and (D) in the case of a beneficial owner, have submitted a demand that (x) reasonably identifies the holder of record of the shares for which the demand is made, (y) is accompanied by documentary evidence of such beneficial owner’s beneficial ownership of stock and a statement that such documentary evidence is a true and correct copy of what it purports to be, and (z) provides an address at which such beneficial owner consents to receive notices given by Terns and to be set forth on the verified list to be filed with the Delaware Register in the Delaware Court of Chancery, will be entitled to receive appraisal rights for the “fair value” of their Shares in accordance with Section 262 of the DGCL. The “fair value” of such Shares as of the Effective Time could be more than, the same as or less than the consideration to be received pursuant to the Merger and Terns may argue in any appraisal proceeding that, for purposes of such proceeding, the fair value of such Shares is less than the Offer Price. The Merger Agreement is more fully described in Section 13 of the Offer to Purchase.

The board of directors of Terns, at a meeting duly called and held, has unanimously (i) determined that it is fair to and in the best interests of Terns and its stockholders for Terns to enter into the Merger Agreement and any related agreements contemplated thereby (“Related Agreements”), to perform its obligations thereunder and to consummate the Transactions, including the Offer and the Merger, (ii) declared the Merger Agreement and the Transactions, including the Offer and the Merger, advisable, (iii) authorized and approved the execution, delivery and performance by Terns of the Merger Agreement and any Related Agreements and the consummation of the Transactions, including the Offer and the Merger, (iv) resolved that the Merger be effected under Section 251(h) of the DGCL as soon as practicable following the consummation (as defined in Section 251(h) of the DGCL) of the Offer, and (v) recommended that the stockholders of Terns accept the Offer and tender their Shares to Purchaser pursuant to the Offer, in each case upon the terms and subject to the conditions set forth in the Merger Agreement.

The Offer and withdrawal rights expire one minute following 11:59 p.m., Eastern Time, on May 4, 2026, unless extended or earlier terminated as permitted by the Merger Agreement (such time or such

subsequent time to which the expiration of the Offer is extended in accordance with the Merger Agreement, the “Expiration Time”).

Purchaser is not providing for guaranteed delivery procedures. Therefore, Terns stockholders must allow sufficient time for the necessary tender procedures to be completed during normal business hours of the Depositary, which is earlier than the Expiration Time.

Purchaser will not be required to accept for payment or, subject to any applicable rules and regulations of the U.S. Securities and Exchange Commission (the “SEC”), including Rule 14e-l(c) under the Securities Exchange Act of 1934, as amended, to pay for any Shares tendered pursuant to the Offer, if any of the conditions set forth in the Merger Agreement are not satisfied or waived in writing by Parent and Purchaser (to the extent waivable by Parent and Purchaser) as of any scheduled Expiration Time, including, among other things, the condition that the number of Shares validly tendered (and not validly withdrawn), considered together with all other Shares (if any) owned by Parent and its affiliates (but excluding Shares that have not yet been “received,” as defined by Section 251(h)(6) of the DGCL), would represent one more Share than 50% of the total number of Shares issued and outstanding as of immediately following the consummation of the Offer. These conditions to the Offer are described in “The Offer—Section 15—Conditions to the Offer” of the Offer to Purchase.

Any stock transfer taxes applicable to the sale and transfer of Shares to Purchaser pursuant to the Offer will be paid by Terns, except as otherwise set forth in Instruction 6 of the Letter of Transmittal. However, federal income tax backup withholding at the applicable rate may be required, unless the required taxpayer identification information is provided and certain certification requirements are met, or unless an exemption is established. See Instruction 8 of the Letter of Transmittal.

If you wish to have us or our nominees tender any or all of your Shares, please complete, sign, detach and return the instruction form below. An envelope to return your instructions to us is enclosed. If you authorize tender of your Shares, all such Shares will be tendered unless otherwise specified on the instruction form. Your prompt action is requested. Your instructions should be forwarded to us in ample time to permit us to submit a tender on your behalf by the Expiration Time.

The Offer is not being made to holders in any jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the laws of such jurisdiction. We are not aware of any jurisdiction where the making of the Offer or acceptance thereof would be prohibited by securities, blue sky or other valid laws of such jurisdiction. If we become aware of any U.S. state in which the making of the Offer or acceptance of Shares pursuant thereto would not be in compliance with an administrative or judicial action pursuant to a valid state statute, we will make a good faith effort to comply with that state statute. If, after a good faith effort, we cannot comply with the state statute, the Offer will not be made to (nor will tenders be accepted from or on behalf of) the holders of Shares in that state. In those jurisdictions where applicable laws or regulations require that the Offer be made by a licensed broker or dealer, the Offer will be deemed to be made on behalf of Purchaser by one or more registered brokers or dealers licensed under the laws of such jurisdiction to be designated by Purchaser.

Instruction Form with Respect to

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

TERNS PHARMACEUTICALS, INC.

$53.00 Net per Share of Common Stock

Pursuant to the Offer to Purchase Dated April 7, 2026

THAILAND MERGER SUB, INC.

a wholly owned subsidiary of

MERCK SHARP & DOHME LLC

a wholly owned subsidiary of

MERCK & CO., INC.

The undersigned acknowledge(s) receipt of your letter and the enclosed Offer to Purchase dated April 7, 2026 and the related Letter of Transmittal (together, as may be amended or supplemented from time to time, the “Offer”), in connection with the offer by Thailand Merger Sub, Inc., a Delaware corporation (“Purchaser”) and a wholly owned subsidiary of Merck Sharp & Dohme LLC, a New Jersey limited liability company (“Parent”), to acquire all of the outstanding shares of common stock, par value $0.0001 per share (the “Shares”) of Terns Pharmaceuticals, Inc., a Delaware corporation (“Terns”), for $53.00 per Share, in cash, without interest, subject to any applicable withholding of taxes and upon the terms and subject to the conditions set forth in the Offer.

The undersigned hereby instruct(s) you to tender to Purchaser the number of Shares indicated below (or if no number is indicated below, all Shares) held by you or your nominees for the account of the undersigned, upon the terms and subject to the conditions set forth in the Offer furnished to the undersigned. The undersigned understands and acknowledges that all questions as to the validity, form and eligibility (including time of receipt) and acceptance for payment of any tender of Shares made on my behalf will be determined by Purchaser in its sole discretion.

The method of delivery of this Instruction Form is at the election and risk of the tendering stockholder. This Instruction Form should be delivered to us in ample time to permit us to submit the tender on your behalf prior to the expiration of the Offer.


Number of Shares to be Tendered:				SIGN HERE

Shares*				Signature(s)

Dated				Name(s) (Please Print)

				Address(es)

				(Zip Code)

Area Code and Telephone Number

Taxpayer Identification or Social Security Number

* Unless otherwise indicated, it will be assumed that all Shares held for the undersigned’s account are to be tendered.