NOT JUST a new mayor but a new D.C. legislature will be sworn in next Jan. 2. Residents of every ward of the city will be voting for two citywide council nominees in primary elections on Sept. 11 -- for chairman and an at-large member -- and then for chairman and for two candidates from the at-large member pool in the Nov. 6 general election. In addition, voters in Wards 1, 3, 5 and 6 will choose ward representatives. That's a total of seven of the 13 council seats up for election this year. If any current holdover council members win their bids for mayor, council chairman or delegate to the U.S. House, their seats may open later.

The departure of council chairman David Clarke guarantees a new legislative leader. John Wilson, now a council member from Ward 2, has earned strong support across the city and is the acknowledged frontrunner to succeed Mr. Clarke. Democrat Vincent Orange and D.C. Statehood candidate Dennis L. Fitch will have to go some to make their cases. All council members will be under pressure to cut spending and even to raise revenues as the city confronts a serious cash shortage. Mr. Wilson, who heads the council's finance and revenue committee, has for years been combing the top ranks of the bureaucracy and making lists of positions he concludes are not needed.

The other two citywide seats up for election will be filled in two stages, since the law doesn't permit both to be occupied by members of the same political party. One is being vacated by Betty Ann Kane, who is running for delegate to the House. The best known candidates in the Democratic contest are (in alphabetical order) Johnny Barnes, a former longtime congressional aide to Del. Walter Fauntroy who ran unsuccessfully against Mrs. Kane in 1982; Linda Cropp, a school board member who made an unsuccessful bid for council member Charlene Drew Jarvis's Ward 4 seat in 1988; and Terry Lynch, president of the Downtown Cluster of Congregations.

The second at-large seat being contested is occupied by Statehood Party member Hilda Mason, who will be her party's nominee for reelection in the November voting. For that round, all voters will be eligible to pick two candidates from a list that will have the Democratic, Republican and Statehood primary winners and any independents who have filed.

For the September primaries, residents registered as independents may not vote. Since the bulk of the decision-making is on the agenda then, residents who want a full voice should sign up for a primary before registration for the primary closes Aug. 13.

The other helpful step is to watch the candidates closely. How would they relate to the new mayor? What should the council do about the shape of downtown and the surrounding neighborhoods? About race relations, the bureaucracy, taxes, the homeless, health care and schools? What laws should be enacted, rescinded or amended? The council elections of 1990 promise to be the most important since the council was established.