NOW THAT Marion Barry is no longer the mayor and is appealing his misdemeanor conviction on a cocaine possession charge, what will he do for a living? Unfortunately, one possible answer to this question focuses on a public institution in the city that hardly needs a new surge of controversy -- the University of the District of Columbia.

First, the UDC trustees were told that a proposal might come their way to hire Mr. Barry for a faculty position. The trustees decided against accepting the proposal, arguing that they have no role to play in specific faculty appointments, as indeed they do not, although they certainly have an overall concern for the welfare of the university.

Barry supporters then went to the political science and urban affairs departments at UDC and were rebuffed in both places by faculty members opposed to the hiring of Mr. Barry. Finally, the chairman of UDC's criminal justice department, Kelsey Jones, said he was planning to offer Mr. Barry a job teaching seniors studying public and social policy. Because Mr. Barry would be a temporary employee, teaching for only a half-year, approval by the department's faculty would not be required. The appointment requires approval by the dean of the college of liberal arts and by the UDC president, and faculty leaders are strongly against it.

Those in favor of the appointment say Mr. Barry's rich community and official experience should be tapped. One trustee added, "There is no dignity in this. He will earn far less than a tenured professor, less even than an executive secretary. He could have earned that much as a public speaker, if anyone wanted to listen to him. That he even needs this post is an example of the man's downfall. He could have had so much more."

But other considerations are more pressing. UDC is a taxpayer-funded institution that is trying to escape the unhappy condition in which it was put in part by some of the appointments and decisions of Marion Barry. Just now, when the school seems to be achieving some credibility in the eyes of its students and the public, is not the time to hire an ex-mayor who has a six-month prison term hanging over his head and who spent years acting out his contempt for the law to teach criminal justice, of all things. The university is too important to its students and the city to permit that.