The Arlington County Board's Republican majority voted Saturday night to name insurance executive S. J. (Sim) Pace to the county school board, replacing one of the GOP's most vocal critics -- Democratic activist Ann C. Broder.

Although Pace will not officially be appointed until May, the action had been anticipated since County Board member Walter L. Frankland Jr. announced he would nominate Pace, 38, to take Broder's seat. A political independent, Pace ran last year for the County Board with Republican endorsement losing to Democrat John W. Miliken.

Control of the public schools has been a key political issue in Arlington since 1975 when Frankland launched his political career by blasting the liberal Democrat coalition that had controlled both the County Board and the school board for years.

Frankland has claimed that the Democrats allowed the quality of Arlington's schools to deteriorate and said one of the GOP's goals is to replace Democratic school board members with appointees who, like Pace, favor traditional methods of instruction.

Pace's appointment will leave Torrill B. Floyd as the only Democratic appointee on the five-member school panel. Republicans had said they wanted to select Pace early so he could help pick a new superintendent to replace Larry Cuban, who is quitting his job in Marh to accept a federal study grant.

A plain-spoken woman with an acerbic wit, Broder, 51, was appointed to the school board in 1973 and served as its chairman twice, an experience she has described as "rotten" because of the job's long hours and incessant demands.

Nevertheless, Broder, wife of Washington Post political writer David S. Broder, is the only person in recent years to serve two four-year terms on the school board. In 1977, when she was nominated for a second term, both Frankland and Dorothy T. Grotos voted against her. Broder, in turn, branded Frankland's repeated attacks on the school system and on superintendent Cuban as "stupid" and "self-serving."

Reached yesterday as she was preparing a party for Cuban, Broder called Pace "a very able young man" but criticized the process by which he was selected. Broder said that although the County Board had invited individuals to apply for the school board, "There is a general perception that the decision had already been made."

That criticism was echoed by board member Milliken, who urged that the school board selection be deferred until May. The Republicans angrily rejected his criticism but agreed to delay appointing Pace until then. Broder's term does not expire until July 1.

Voting for Pace were Republicans Frankland, board chairman Stephen H. Detwiler and vice chairman Grotos. Democratic board members Milliken and Ellen M. Bozman did not vote.