IT WOULD be easy to assume that the University of the District of Columbia is unprepared to address its serious fiscal problems, leadership deficiencies and seemingly biennial search for a new president. The chairman of its board of trustees is gravely ill, and the makeup of the entire board may undergo drastic changes within the next few months. Its cash reserves are gone, and the university may face even greater budget cutbacks in the very near future.

But the fact is that a strong nucleus of dedicated trustees, including the board's newly installed vice chairman, the Rev. A. Knighton Stanley, has promising ideas that could greatly improve the board's performance as well as aid in the search for the sixth UDC president in 12 years. Among other things, the trustees have approved budget changes that will save millions of dollars, while still meeting a key demand of disgruntled students by doubling the number of open hours at the university's main library. And the D.C. Council has also begun to take a welcome and far more active oversight role in these matters despite the fact that its own leadership is about to change hands.

One particularly good idea, under consideration by both the D.C. Council and the trustees, would be to enlist the services of the Washington-based Association of Governing Boards of Universities and Colleges. The association can provide important advice on how the UDC trustees can move away from an overly intrusive management of the university and embark on a more effective policy-making role. At a time when the university's leadership is in flux, the association could also use its search consultation service to help UDC find a strong president.

There is one thing the university clearly does not need at this time -- more trustees. But the D.C. Council is considering legislation that would raise the number of trustees from 15 to 21. The council should consider other changes, such as ending the divisive practice of having three trustees from the alumni associations of the three schools that were merged to form UDC. Two slots on the board could be reserved for members who are elected by UDC's alumni, and one more student board member could be added, perhaps from UDC's graduate programs.

One other change would strengthen UDC's board of trustees. Eleven of its members are appointed by the mayor with the approval of the D.C. Council. These positions must now be treated less as rewards for political loyalty and more as a means to provide shrewd educational guidance to the university.