District Democrats last night chose Ted Gay, 38, a manufacturer of picture frames whose approach to local politics has always been low-key, as chairman of the D.C. Democratic State Committee -- a much more subdued organization with Republicans now running the White House and the U.S. Senate.

Gay was elected unanimously by the normally contentious committee, with the strong support of the local party's outgoing chairman, high-profile attorney Robert B. Washington Jr. Washington, 38, did not seek reelection after heading the committee -- which sets policy for the local party and sometimes fills interim seats on the City Council -- for the last five years.

Gay, a compromise candidate who lacks Washington's flamboyance but is known as an indefatigable grass-roots worker, easily survived during the past several weeks a prevote challenge for the chairmanship by William H. Simons, president of the Washington Teachers Union and leader of a faction of the committee that has consistently opposed Washington's leadership. Washington defeated Simons for chairman last year in a hard-fought contest.

Before last night's election, committee sources said, Gay had 28 of the committee's 54 members solidly committed, with about 10 committed to Simons. Washington's friends on the committee said last night that they lobbied intensely for the unanimous vote, with one saying it was "to teach Bill Simons a lesson." The sometimes abrasive Simons did not attend last night's meeting.

Some committee members took the election of the soft-spoken, rarely controversial Gay as a sign of a lack of intense interest in the Democratic Party here, which makes up more than three-fourths of the D.C. electorate but has been much less visible since the Republican Party took such firm control of federal Washington last November. Gay's term is for one year.

"Is there still a party?" asked committee member Paula Nickens, who voted for Simons in his defeat last year. "Is there anything for us to do? We'll see."

Said one Gay backer who asked not to be named: "Ted is a hard worker, and he's been there when we needed him. He has no presence, but we'll be all right."

Washington said he decided not to run again because he no longer could spend the time required to be chairman. He is now a partner with the Washington office of the New York law firm of Finley, Kumble, Wagner, Heine, Underberg and Casey, which recently merged with his old local firm, Danzansky, Dickey, Tydings.

But Washington will remain on the committee, and he said of Gay last night, "He's always been on our team." Washington said he plans "to be active in the 1982 mayor's race, and although he gives up his automatic seat on the Democratic National Committee he still will serve on two of the national board's commissions.

Gay, a small businessman who manufactures picture frames and lives just off Capitol Hill in Northeast Washington, said he would seek to make the local party rejuvenate itself through grass-roots ward organizations.

"It seems we're out of touch with the nation," he said. "The way we're going to get back in touch is from the ground up."

Also last night, Barbara Bell Clark, a longtime committee member and Washington supporter, was reelected vice chairman; Paul Kuntzler, a leading gay activist, was named recording secretary; school board member Barbara Lett Simmons was named corresponding secretary, and Walter Beach was named treasurer.