红河银行股公司美股招股说明书(2025-10-24版)

(to Prospectus dated November 20, 2024) Up to 928,557 Shares ofCommon Stock Offeredby the Selling Stockholders The following information amends and supplements information contained in the prospectus, dated November 20, 2024, asamended, relating to the offer and sale by (a) Red River Bancshares, Inc. of common stock, preferred stock, depositary shares, debtsecurities, warrants and units, in one or more offerings, up to a total dollar amount of $100,000,000, and (b) the selling stockholdersnamed in the prospectus of up to an aggregate of 928,557 shares of common stock. This prospectus supplement should be read in conjunction with the prospectus and all amendments thereto, and is qualifiedby reference to the prospectus, except to the extent that the information that is presented herein supersedes the information containedin the prospectus. This prospectus supplement is not complete without, and may only be delivered or utilized in connection with, theprospectus, including any amendments or supplements thereto. Investing in our securities involves risks. You should carefully consider the Risk Factors referred to on page 7 of theprospectus and set forth in any applicable prospectus supplement and in the documents incorporated or deemed incorporatedby reference herein before making any decision to invest in our securities. These securities are not savings accounts, deposits, or other obligations of any bank and are not insured or guaranteedby the Federal Deposit Insurance Corporation or any other government agency. Neither the Securities and Exchange Commission nor any state securities commission nor any other regulatory bodyhas approved or disapproved of these securities or passed upon the adequacy or accuracy of this prospectus. Anyrepresentation to the contrary is a criminal offense. The date of this prospectus supplement is October 24, 2025. SELLING STOCKHOLDERS The following information is being provided to update the stockholder table and related narrative discussion in the prospectusto reflect the sale by S3 Dynamics, L.P. of 236,000 shares of common stock on October 23, 2025. The information set forth in thenarrative discussion and table below supersedes and replaces the information in the prospectus under the section entitled “SellingStockholders.” The following table sets forth to our knowledge, certain information about the selling stockholders as of October 23, 2025,based on information furnished to us by the selling stockholders regarding the beneficial ownership of shares of our common stockand the number of shares of our common stock that may from time to time be offered or sold by them pursuant to this prospectus.Beneficial ownership is determined in accordance with the rules and regulations of the SEC. The number of shares beneficially ownedbefore the offering is based on the number of shares of our common stock owned by the selling stockholders. The informationregarding shares beneficially owned after the offering assumes the sale of all such shares that are offered by the selling stockholdersand that the selling stockholders do not acquire any additional shares. Percentage of beneficial ownership is calculated based on6,576,609 shares of common stock outstanding as of July 31, 2025. (1)Consists of 266,407 shares of Common Stock held of record by the John Charles Simpson Jr. Irrevocable Trust UA 25-NOV-03 (“JCSJ Trust”) and 167,239shares of Common Stock held of record by the Angela Katherine Simpson Irrevocable Trust UA 25-NOV-03 (“AKS Trust”). Simeon A. Thibeaux is the soletrustee of the JCSJ Trust and the AKS Trust and has sole voting and sole dispositive power over these shares.(2)Shares are held by S3 Dynamics, L.P. The sole general partner of S3 Dynamics, L.P. is S3 Management, L.L.C. which has management authority over S3Dynamics, L.P. and Mr. Thibeaux is one of three managers of S3 Management, L.L.C. Mr. Thibeaux is also the trustee or an investment advisor of trustsowning 100% of the limited partnership interests in S3 Dynamics, L.P. Mr. Thibeaux has shared voting and shared dispositive power over these shares. Information concerning the selling stockholders may change from time to time and any changed information will be set forthin supplements to this prospectus, if and when necessary. The selling stockholders may offer all, some, or none of their shares ofcommon stock. We cannot advise you as to whether the selling stockholders will in fact sell any or all of such shares of common stock.In addition, the selling stockholders may have sold, transferred, or otherwise disposed of, or may sell, transfer, or otherwise dispose of,at any time and from time to time, shares of our common stock in transactions exempt from the registration requirements of theSecurities Act after the date on which they provided the information set forth in the table above. We will pay all expenses of the registration of the shares of our common stock to be offered by us and the sellingstockholders un