BECAUSE OF Mayor Anthony Williams's dawdling in nominating replacement trustees, the unacceptable is about to occur at the University of the District of Columbia. From next Monday, the $40 million District-owned school with more than 5,100 students will not have a functioning board of trustees.

As long ago as May, officials responsible for D.C. boards and commissions knew that the university trustee board would soon be without a full house. At the time, the 15-member board had 11 serving members, enough to constitute a quorum. The Williams administration also knew that the terms of four sitting members would expire in mid-May, and that their authorized 180-day holdover status would end on Nov. 15. Despite a seven-month warning, a majority of UDC's governing body will leave office next Monday without their replacements having been nominated.

The delay has placed both the D.C. Council and the university in a difficult position. Even if the mayor produces a list of proposed trustees this week, the council will not have enough time to properly weigh their qualifications and fitness. D.C. Council member Kevin Chavous (D-Ward 7), chairman of the education committee, has agreed to hold hearings on Nov. 29, provided the mayor finally does his part. But by that schedule, the earliest the council could act would be at its December meeting.

In his defense, the mayor contends he's been having trouble attracting "the best people, people of national stature," to UDC because of the school's well-known problems. That may be so. But judging from some of the local names being bandied about (former council member Bill Lightfoot and the Rev. Willie Wilson, for two), the vigor of Mr. Williams's talent search is open to question. So too, in the light of this episode, is his commitment to UDC.