At 9:20 p.m. the phone rings in the crowded International Hotel suite. It's Ted Kennedy, someone says. "What!" says an incredulous David A. Clarke, the District of Columbia's new City Council chairman-to-be.

Clarke stumbles in a rush across the room to the phone, grasps it with two hands. "Is this Ted Kennedy? . . . . How are you? . . . . Well, thank you for calling! . . . . Well, I'm honored by your attention . . . . Okay, good luck to you, too!"

Clarke is openly excited. Suddenly, after eight years as a City Council member from Ward 1, he has been catapulted into the number two political job in the District. Suddenly he is a big man, an important man, coming from far behind to win overwhelmingly against two political pros, Sterling Tucker and incumbent Arrington Dixon, who had each held the citywide chairman's post.

Clarke had run as a man of the people, a champion of the poor, the tenants, the jobless, the little man beset by Reaganism. He had run as a dedicated liberal, a concerned white man in a largely black city. It was clear the call from Kennedy was very special.

Excitement is not Clarke's typical personal style. He is an intense giant of a man -- 6-5 and 250 pounds -- who seemed on election night Tuesday to go out of his way to appear low-key, laid back. That night he spoke quietly, smiled frequently, stayed cool. He has penetrating blue-green eyes that fix on the person he is speaking to. In City Council meetings, he is sometimes given to angry outbursts.

His victory -- with 44 percent of the vote in the three-way race -- had seemed a sure thing since 8:31 p.m. Tuesday, when a local television station showed early returns giving him 48 percent of the vote against 26 and 25 percent for his opponents.

At that moment, Clarke was taking a shower in his rambling Mount Pleasant row house that doubled as a campaign headquarters. When he came downstairs in brown slacks and a beige shirt open at the neck, his black curly hair slicked back with water, his wife Carole and son Jeff and a dozen neighbors and campaign volunteers stood and cheered wildly.

"All right! We want 60 percent!" they shouted.

Clarke smiled. He made no formal statement to the group of supporters -- black, white and Hispanic -- who were having spaghetti and meatballs in the dining room crowded with boxes of voter index cards and campaign telephones. Apparently feeling some formality was required, he turned to a reporter and said quietly, "It looks like I'll pull through. I'm especially pleased because the size of the vote will give me a clear mandate which I wanted . . . . We may be over 50 percent."

Then he went and crouched in a corner and tried to get a tape recorder to work. It was complicated but, unruffled, he began reading a long instruction sheet. Nobody volunteered to help him, and he didn't ask. Finally he abandoned the effort.

Most of the insiders at his house were casually dressed in Dave Clarke T-shirts and faded jeans. One, Richard Siegel, said he is a neighbor and volunteer. "Dave's campaigns are unusual," he said. "It's a groundswell of volunteers, various people working hard." Another volunteer, a student named Dwight Locke, said, "I put in 12 hours a day. I live in this ward and became interested in Clarke when I started reading he was for rent control and senior citizens."

Carole Clarke, at first wearing jeans and T-shirt, went upstairs and returned wearing an elegant cotton print dress. She looked a bit like Jane Fonda and spoke warmly in a broad Massachussetts accent.

Just before 9 p.m. everyone piled into cars to go down to the victory party at the International Hotel on Thomas Circle. Clarke, Carole and Jeff piled into his battered 1977 Toyota Celica. Clarke slouched in the driver's seat. The car's innards growled like a truck. A "electro sensor" on the dashboard flashed an urgent red message: "LINING WEAR." Occasionally an "ENGINE OIL" light flashed on.

Halfway down 16th Street, a crisis. The list of phone numbers of other candidates has been left at home, Carole said. Clarke started to turn around, but Carole grabbed for the car phone, caught someone still at the house and asked him to bring the list. "If I'm gonna be the chairman I've got to call up people and congratulate them," Clarke explained to 7-year-old Jeff. In the ensuing turmoil of the evening, the list never appeared.

A TV crew waited at the hotel entrance. Clarke waved as he went by on his way to park the car in the basement. The crew sprinted after him. Other crews and reporters gathered around. "I look forward to working with all my colleagues on the council ," Clarke said. "We worked very hard. We started way from behind. We never stopped going. We never let up the energy . . . . My relationship with Mayor Barry is very good."

He was speaking as the clear victor. It was 9:10 p.m.

Minutes later, in a private suite upstairs, Clarke received the call from Kennedy.

At 9:42 he decided it was time to go downstairs to the big crowded ballroom and make a victory statement. "Okay, let's go!" he said.

There were 500 people down there, about two-thirds of the crowd white and one-third black. They were having quiche and chocolate cake and beer and white wine, and they all went wild with cheers and applause when Clarke and his family walked in.

Clarke made his way to the other side of the room, shaking hands and receiving congratulations in his low-key way, calling most people by their first names. When he began speaking at 9:50 p.m. he was smiling broadly and he said, "What can you say? It's a hell of a lot better than being a distant third! We've come a long way!"

Later in the evening Sterling Tucker came to the ballroom and made a graceful concession statement. "I've known Dave Clarke for a long time," he said. "We were in the civil rights movement together . . . . He loves this city and its people . . . . You'll be proud of him."