Six Arlington residents met yesterday's deadline for applying to the County Board for appointment to the School Board seat being vacated June 30 by Simone J. Pace.

Pace, one of the two remaining Republican appointees on the five-member School Board, is not seeking reappointment to a second four-year term. He was chairman of the board last year before Democratic appointees gained control of three seats.

Pace yesterday likened his decision not to seek another term to climbing Mount Fuji: "As someone once said, 'You're a fool if you don't climb it once and you're a fool if you climb it twice.' Besides, no one on the County Board has asked me" to seek another term. The County Board is controlled by Democrats.

School Board members are paid $5,000 a year. In recent years vacancies have attracted more than 20 applicants. The County Board is scheduled to appoint the new member May 18.

The applicants are Barbara E. Baker, a former president of the Barrett Elementary School PTA; Allan V. Burman, an employe of the U.S. Office of Management and Budget, who is a former Key Elementary School PTA president, and Judy Connally, a free-lance planner and writer who has worked on advisory committees on instruction and for programs for gifted and talented children. Also, Robert E. McClendon, a Peace Corps administrator who has served on the County Council of PTAs committees dealing with the budget, teacher career ladders and the "Nation at Risk" report; David A. Walden, a naval architect, and Jo Winkelman, who has served on task forces on computers, early childhood education and the needs of children who do not speak English.