About 750 faculty members and students of the University of the District of Columbia yesterday cheered a strong appeal for unity by the new university's president, Lisle C. Carter Jr.

Carter's speech was interrupted by a small group of demonstrators in the front row of the Dunbar High School auditorium who beat on drums, threw eggs at the platform and taunted the president as he promised to make the university a "first-rate institution."

When three protesters were led away by police, the audience applauded loudly.

When Carter finished his 40-minute speech he received a standing ovation. Among those clapping enthusiastically were some of Carter's strongest critics who participated in a two-day faculty strike earlier this month at the university's Van Ness campus (which formerly was Washington Technical Institute).

Washington police said last night they had arrested one protester, James C. Palmore, 36, who identified himself as a student for the past 10 years in the music department at Federal City college. Palmore was charged with disorderly conduct.

The new university, which officially began last August, is being formed by a merger of the city's three public colleges -- Federal City, Washington Tech and D.C. Teachers College.

Carter said that despite the strike, which was prompted by a new city law permitting the university to make temporary appointments, all academic departments at the three colleges would be merged by next fall.

Some prefoeesors will have to move to different campuses, he said, but Carter promised that the exact shape of consolidated program would be worked out by faculty members themselves who are serving on 42 planning committees.

"The (planning) process is widely participative and we are seeking ways to strengthen it," Carter declared. "But. . . in the short run participation increases anxiety because it sharpens conflict and heightens the uncertainty of outcomes."

Carter announced that partly in response to faculty requests the university was asking the city government for $4 million more for its Van Ness campus, for which $68.3 million already has been appropriated.

University vice president Claude Ford said the money was needed for more laboratories and science equipment and a larger library.

In addition, Carter said the university would continue to press for congressional approval of $56.7 million to build a second campus at Mount Vernon Square.

The two campuses together will be able to house 13.300 full-time equivalent students, about 45 percent more than the 8,524 full-time equivalent students currently enrolled.

University enrollment has dropped about 13 percent over the past two years, but Carter said he was convinced that it would rise steeply by 1984 as more D.C. high school graduates are attracted to the college.

After Carter's speech, Judy Smith, president of the faculty Senate at the Van Ness campus said that over the past few months distrust among administrators, faculty members and students has become so great that "nobody believes anything that anybody says." There must be "a reciprocity of trust on all sides," she said.