Clene (CLNN) 424B5 Prospectus supplement for primary offering

Filed Pursuant to Rule 424(b)(5)

Registration No. 333-264299

SUPPLEMENT NO. 1 TO PROSPECTUS SUPPLEMENT

DATED MARCH 7, 2023

(To Prospectus dated April 26, 2022)

Clene Inc.

This Supplement No. 1 to the Prospectus Supplement supplements and amends the Prospectus Supplement dated March 7, 2023 (the “Prospectus Supplement”) filed by Clene Inc. (“we,” “us,” and “our”). This Supplement No. 1 to the Prospectus Supplement should be read in conjunction with the Prospectus Supplement and the base prospectus dated April 26, 2022 (the “Base Prospectus”).

We have previously entered into a Purchase Agreement (the “Purchase Agreement”), dated March 3, 2023, with Lincoln Park Capital Fund, LLC (“Lincoln Park”), relating to the sale of up to $25,000,000 in shares of our common stock and an additional 499,002 shares of our common stock issued as commitment shares to Lincoln Park.

We filed the Prospectus Supplement to register the offer and sale of the following securities issuable pursuant to the Purchase Agreement: (i) up to $25,000,000 in shares of our common stock and (ii) an additional 499,002 shares of our common stock issued as commitment shares to Lincoln Park. We issued shares of our common stock pursuant to the Purchase Agreement and the Prospectus Supplement for gross proceeds of approximately $434,700. An aggregate of approximately $24,565,300 of shares of our common stock remained to be sold under the Purchase Agreement and the Prospectus Supplement at the time it was terminated.

The purpose of this Supplement No. 1 to the Prospectus Supplement is to terminate, effective on the date of this Supplement No. 1 to the Prospectus Supplement, the offering of the approximately $24,565,300 of shares of our common stock that were not sold under the Purchase Agreement prior to its termination and the Prospectus Supplement.

The date of this Supplement No. 1 to the Prospectus Supplement is June 16, 2023.