Directors of Riggs National Bank yesterday elected Jackson B. Gilbert vice chairman and a member of the board in a move designed to give him broader executive responsibilities in the institution's new management structure, the bank announced.

Gilbert, 50, had been a member of the senior management team at Morgan Guaranty Trust Co. of New York before he was appointed executive vice president of Riggs in February.

As vice chairman, Gilbert's responsibilities will continue to include supervision of Riggs' international division, with particular emphasis on lending activities.

Gilbert had been president of Morgan Guaranty International Finance Corp. before coming to Riggs. As president of the Morgan Guaranty division, he was responsible for investments in banks and financial institutions in about 35 countries.

It wasn't made clear how far Gilbert's additional responsibilities as vice chairman will range in Riggs' reorganization of its management team, which began with a shakeup earlier this year.

In a brief prepared statement, Riggs Chairman and Chief Executive Officer Joe L. Allbritton said Gilbert "has amply demonstrated during the last few months the special talents and expertise which will add to the already substantial strength of our management team."

Gilbert is the second vice chairman to be named this year. Earlier, Thomas W. Wren, a long-time Allbritton associate, was appointed vice chairman of the bank's board.

Wren had been president of University State Bank and University Bancshares Inc.--banking interests owned by Allbritton in Houston--when he was elected vice chairman of Riggs' parent company, Riggs National Corp., in 1981.

Allbritton announced earlier this month that he plans to sell the two banks owned by University.

Riggs officials did not elaborate yesterday on the separation of responsibilities of the two vice chairmen.