D.C. City Council member David A. Clarke, who trailed badly at the outset of the campaign for council chairman, has surged into the lead, ahead of incumbent Arrington Dixon and former chairman Sterling Tucker, according to a new Washington Post poll.

The Post poll found 32 percent now supporting or leaning to Clarke compared to 23 percent for Dixon and 21 percent for Tucker. About a fourth of the respondents -- 24 percent - said they were undecided, and their movement could affect the outcome of the election.

The field of candidates now is almost exactly the reverse of a Post poll taken in June, which showed Tucker with 31 percent, Dixon 28 percent, Clarke 16 percent and about 25 percent undecided.

In the new poll, conducted Wednesday and Thursday and consisting of re-interviews with 813 of the 1,374 interviewed in June, more than half the respondents had changed their positions since the first interview -- fluidity in voter preference that also could affect the outcome of Tuesday's election.

The key difference between the candidates' rankings in June and now is that Dixon and Tucker appear to have kept less than half their initial support while Clarke has kept almost three-fourths of his early backers and picked up most of the fall-off from the other two.

Clarke's lead is largely accounted for by a move toward him from white voters who tended to ignore his campaign in June. At that time, according to the Post's earlier poll, 22 percent of white voters supported Clarke, slightly fewer than supported Dixon and Tucker. The largest single group of white voters was undecided then.

In the new poll, Clarke gets 53 percent of the white vote while Dixon and Tucker draw 17 percent apiece.

But Clarke has shown sharp improvement among black voters as well. The poll showed 25 percent for Clarke, 26 percent for Dixon, 23 percent for Tucker and the balance undecided.

Support for Clarke among those interviewed increased in direct relation to income, with his highest level of support among those households with annual incomes of $30,000 or more and among college graduates. Tucker was the strongest candidate among those with less income, while Dixon's support was distributed almost evenly across income and education groups.

Clarke, speaking from a telephone in his car en route to Georgetown for one of numerous events he attended yesterday, said he plans to guard against overconfidence in the closing days of the contest. "The only poll that counts is Sept. 14," he said.

Tucker, who also was taking part in several events yesterday, noted that the poll was completed before he was endorsed Friday by the editorial page of The Washington Post, which his campaign considers a critical boost. "This," Tucker said of the polling, "is obviously before my momentum, before the weekend."

Dixon, who spent much of yesterday at a rally and in a motorcade in Ward 4 and in another motorcade in Ward 8, said he still feels confident of victory. "It is clear the presence of Mr. Tucker in the race is having an effect of potentially splitting the race," he said. "The voters can take him out by voting for me, which is what they should do. "

The poll indicates Clarke is leading in Ward 1, which he represents on the council, and Wards 2, 3 and 6 -- essentially the same coalition of white and moderate-income blacks that boosted Marion Barry to a come-from-behind victory over Tucker and former mayor Walter E. Washington in the 1978 Democratic primary for mayor.

In addition, Clarke is showing stronq support in Wards 4, 5 and 7, the ring of moderate to upper-income black neighborhoods in Northwest, Northeast and Southeast Washington where 50 percent of the votes in the 1978 Democratic primary were cast.

Clarke runs even with Dixon in Ward 4, the ward Dixon represented on the council from 1975 to 1978, when he was elected chairman. Tucker, who lives in Ward 4, trails the other two there.

Each of the three candidates has about a quarter of the vote in Wards 5 and 7, Dixon showed a surprising lead in Ward 8. Tucker, who in the early poll led in four of the eight wards, now trails in six wards and is even in two wards. Clarke doubled his support among voters over 30 years of age.

The earlier Post poll indicated that more than 55 percent of the voters did not know Clarke well enough to form an opinion about him, even though the 38-year-old lawyer and former civil rights actiVist has been a member of the City Council for eight years.

Clarke, who had the private encouragement of Barry and is considered one of the most activist members of the council, has since put together a string of endorsements from labor groups, community and housing activists, Democratic organizations and political clubs.

He also has based his campaign on a record of firm, though sometimes controversial, stands on housing and criminal justice issues, and appeals to voters throughout the city who identify with those stands or who have been affected by those issues.

Dixon, a 39-year-old former computer science professor, has raised the most money of the campaign, about $170,000,compared to about $100,000 each by Clarke and Tucker. He has the largest campaign staff and has portrayed his candidacy as a call for continued better management of the city's 13-member legislature.

His campaign, based on a slogan of "Defending the Dream," has also emphasized the role of the chairman as a leader in the face of Reagan administration budget cuts. Still, his campaign has shown limited movement and he has not been able to completely shake allegations of a runaway council under his leadership.

Tucker, a 59-year-old former assistant secretary of Housing and Urban Development and longtime civil rights activist who entered the race late after aborting a second try for mayor, has been plagued by uncertainty about which office he wants to run for and a faltering campaign organization.

As the campaign draws to a close, however, Tucker has obtained several endorsements and significant financial support from trial lawyers in the city, many of whom say they are backing him because of his opposition to a no-fault auto insurance bill supported by Dixon and approved by the council earlier this year.

In another weekend campaign development, Tucker said he is cancelling a radio ad that has played for several days. The one-minute ad five times accuses Dixon and Clarke of being "soft on crime" and calls on voters to "make our city safe again."

Asked about the ad, Tucker declined to point to any action that either Dixon or Clarke had taken on crime that he did not like. He said it is being replaced with an ad on his endorsements.

Former U.S. attorney and Watergate prosecutor Earl Silbert released a letter to Clarke on Friday that said, "you are not soft on crime nor did you bottle up legislation."

As the three candidates for chairman headed into the final 72 hours of campaigning, the races for two at-large seats and four ward level seats on the council also were winding up.

Incumbent Democrat Betty Ann Kane, who earlier this year dropped out of the mayor's race, is running for reelection to her council seat against two challengers, congressional aide Johnny Barnes and Barbara Lett Simmons, a school board member.

Council member Hilda Mason is running unopposed for the Statehood Party nomination.

In Ward 1, housing activist Marie Nahikian and school board member Frank Smith are leading candidates in a crowded field of Democrats seeking to replace Clarke. The others are Reuben Lewis, a financial analyst; Calvin O. Wingfield, a U.S. Department of Agriculture employee; and Glenn L. Reitze, an attorney.

Three candidates are vying for the Republican nomination, former elections board chairman Charles Fisher, ANC commissioner Nancy Shia and Jacob Sherrill Jr., an accountant.

In Ward 3, Democratic council member Polly Shackleton is facing a spirited battle for reelection from Ruth Dixon, a former League of Women Voters president, and Mark Plotkin, a political consultant making his first bid for elected office. Lois DeVecchio is unopposed for the Republican nomination.

Ward 5 Democratic incumbent William Spaulding is trying to turn back strong bids by former at-large council member Douglas Moore and civic activist Robert I. Artisst. Other candidates are Robert King, former director of the 14th Street Project Area Committee, and Richard S. Lee, a Northeast florist. The winner will face Republican W. Ronald Evans, who is unopposed.

In Ward 6, Democratic incumbent Nadine Winter faces John Warren, who currently represents Ward 6 on the school board.