Riggs National Bank has announced the election of four new members to its board of directors, bringing to seven the number of new members added since Joe. L. Allbritton gained operating control of the area's largest banking company in August.

The four new directors, boosting the board's membership to 23, are Martin Atlas, Lawrence I. Hebert, Charles F. Spalding and Jack Valenti, according to Vincent C. Burke Jr., the bank's chairman and chief executive officer. Allbritton is chairman and chief executive officer of Riggs National Corp., holding company for the bank.

Atlas is executive vice president and director of Cafritz Co., Cafritz Construction Co. and Ambassador Inc., all located in Washington. He is also vice president and director of the Morris and Gwendolyn Cafritz Foundation. An attorney and economist who held several government posts, Atlas also lectures at American University.

Hebert, who has been associated with Allbritton corporate interests since 1970, recently was elected president of Perpetual Corp., the major holding company for Allbritton's financial interests. Hebert also serves as vice chairman of the board of Houston Financial Services Ltd. of London, vice president of University Bancshares Inc. of Houston, and director of Allbritton Communications Co. of Washington.

Valenti is president of the Motion Picture Association of America, the Motion Picture Export Association of America and the Association of Motion Picture & Television Producers. Prior to assuming his current duties in 1966, Valenti served as special assistant to President Lyndon B. Johnson.

Spalding, currently engaged in private investing, served as vice president of the corporate finance division of Lazard Freres & Co. from 1966 to 1977 in New York. Before that, he served as vice president of the television department of J. Walter Thompson.

In August, when Allbritton took over Riggs, both he and Thomas W. Wren, a Houston banking associate, became members of the boards of both the bank and the holding company.

In addition, the next month, Louis Martin, an assistant vice president of Howard University, was named a director. Martin was the first black named to serve on the bank's board.