David A. Clarke, a 38-year-old lawyer, D.C. City Council member and former civil rights activist, scored an impressive victory yesterday in the race for the Democratic nomination for council chairman after having trailed badly in the early weeks of the campaign.

Incumbent chairman Arrington Dixon, who was seeking a second term, and former council chairman Sterling Tucker, who was striving to make a political comeback as a last-minute entrant in the race for his old job, finished far behind the front-running Clarke, who came close to not making the run for chairman at all.

With returns counted in all of the city's 137 precincts, Clarke, a two-term council member from the central city Ward 1, won with 40,702 votes, or about 45 percent. Dixon and Tucker split the rest of the votes with about 27 percent each. Dixon had 25,950 votes and Tucker 24,555. Clarke has no Republican opponent in the Nov. 2 general election.

In the race for the Democratic nomination to an at-large seat on the council, incumbent Betty Ann Kane won over three-term school board member Barbara Lett Simmons and congressional aide Johnny Barnes, the returns showed.

Kane, who earlier this year dropped out of the Democratic race for mayor when she ran out of money, rolled up 56 percent of the vote, with 46,220 votes to 25,669 for Simmons and 10,537 for Barnes.

With the exception of Dixon, a former Ward 4 council member who was elected chairman in 1978, yesterday's balloting appeared to be a vote of confidence for incumbents as Polly Shackleton in Ward 3, William R. Spaulding in Ward 5 and Nadine P. Winter in Ward 6 appeared headed for reelection.

Yesterday's returns -- which do not include some 20,000 challenge ballots yet to be counted -- signaled no significant philosophical change on the council. Clarke has been more closely allied with liberal ideas and groups than Dixon, but the difference, based on the records of the two men, is one of degree rather than of kind. One difference is that Clarke is much closer to Mayor Marion Barry.

Clarke, smiling broadly but appearing very calm at his home-turned-headquarters on 17th Street in Mt. Pleasant, heard the early returns over television at 8:21 p.m.

He joined campaign workers for a spaghetti supper prepared by his wife, Carole, before driving his family in his beat-up Toyota to his election-night party at the International Inn at Thomas Circle. talked as if he were certain of winning.

"The first thing is to get the council together and get the people comfortable with me and comfortable with each other," Clarke, a graduate of George Washington University and Howard University law school and a former lawyer for the Southern Christian Leadership Conference,told reporters outside his hotel before secluding himself in an eighth-floor suite, where he received a call of congratulations from Sen. Edward M. Kennedy (D-Mass.).

He finally emerged at about 10 p.m. to tell supporters, who had been celebrating downstairs over quiche and chocolate cake, "The processes of politics belong to the people." A former seminary student, Clarke asked supporters to pray for him, "so I can use what you have given me."

Clarke, who raised about $100,000 for the race, attributed his apparent victory to a core of volunteers made up of activists in the field of housing and criminal justice who did "incredible campaign work."

After laying the groundwork to run for chairman, Clarke abruptly announced in April that he would not run, citing fears that the race would be overshadowed by the mayoral campaign and that it could be racially divisive -- Clarke is white, and the city's population is about 70 percent black.

A few weeks later, however, Clarke reversed his decision and jumped back into the race when no other candidates announced against Dixon.

Tucker -- who narrowly lost a 1978 campaign for mayor to Marion Barry in 1978, considered another try for that office earlier this year, and was a surprise entrant into the chairman's race in late June -- conceded defeat just before 10 p.m. and then visited Clarke at his headquarters to offer his support in the November general election, in which there is no Republican candidate.

"The people have spoken. I believe in this process. We worked 100 years to get it," Tucker said of yesterday's voting. "David is a bright and able man and I will give him all the support I can. His commitment to the community is deep."

Although Dixon could not be reached for comment early last night, an aide indicated the campaign did not expect to overcome Clarke's huge early lead. "If you're asking me to find a bright spot in this, I can't," the spokeswoman said.

In three of the four ward-level council races, Democratic incumbents apparently won their races for nomination to third terms. Only the Ward 1 council race lacked an incumbent, because of Clarke's decision to forsake his seat to seek the chairmanship.

In the Democratic council primary in Ward 1, school board member Frank Smith, 39, had 4,224 votes, while his closest competitor, 35-year-old Marie Nahikian, had 3,482. The other Democrats in the race were Glenn L. Reitze, 39, an attorney who had 232 votes, Reuben M. Lewis, 38, a financial consultant, who had 142, and Calvin O. Wingfield, 57, a federal employe, who had 156.

In the early 1970s, Smith and Nahikian were allies in the fight to keep real estate speculators from driving lower income blacks and Hispanics out of the ward which is the city's most racially and ethnically mixed community.

"It's close, but I think things are going to get better," Smith said, in cautious anticipation of victory.

However, Nahikian said she will challenge the results. She said she and her campaign workers knew of entire blocks where residents had been left off of voter rolls and were required to cast special ballots.

In the Ward 1 Republican council primary, Charles B. Fisher, former chairman of the city's election board, won over a field of three with 213 votes. Nancy Shia trailed with 83, followed by Jacob Sherrill Jr. with 70.

In the Ward 3 council primary, incumbent Democrat Polly Shackleton, with 5,103 votes, claimed victory over challengers Ruth Dixon, 60, past president of the League of Women Voters and political consultant Mark Plotkin, 35. Dixon had 3,724 votes and Plotkin had 1,900.

Shackleton was thought to be vulnerable this year because of her age and because redistricting last year left her bereft of Georgetown, which had traditionally been her stronghold. Georgetown became a part of Ward 2.

In the November general election, Shackleton was will face Republican Lois DeVecchio, who was unopposed in that primary yesterday.

In Ward 5, Democratic incumbent William R. Spaulding led four challengers, including former council member Douglas E. Moore, who was trying for a political comeback. Spaulding led the field with 4,552 votes, followed by Robert I. Artisst, 48, an associate professor at the University of the District of Columbia, who had 3,973.

Moore, 54, was third with 3,475. Social planner Bob King, 42, trailed with 900, followed by florist Rick Lee, 39, with 855.

Republican W. Ronald Evans, 44, a real estate broker and auctioneer, was unopposed in his party's Ward 5 primary.

In Ward 6, which sprawls from Capitol Hill to Anacostia, Democratic incumbent Nadine P. Winter, who barely retained her council seat four years ago, last night ran comfortably ahead of her lone challenger, school board member John E. Warren, 36. Winter won with 6,561 votes, compared to 4,049 for Warren.