As of Tuesday evening, seven persons had applied to fill the vacancy on the Arlington School Board. The deadline for applications was yesterday.

The County Board is expected to make an appointment Friday to fill the unexpired term of O.U. Johansen, who resigned Sept. 1. The new member will serve the remainder of Johansen's term, until July 1, 1983.

The recent applicants are:

* Paul Fuqua, a lifelong resident of the county who works at Police Science Services Inc. and has been a PTA member at Woodmont Elementary.

* Donald Joseph Hunter, a part-time employee at The Washington Post, who has worked as an election day officer in Arlington and was a member of the Neighborhood Planning Commission when he lived in Washington.

* Paul Gruber, employed at Systems Development Corp. in McLean, who has been a PTA member at Woodmont, Stratford and Washington-Lee, and has served on school board and county board committees.

* Joan K. McDermott, a teacher at Fairfax County Public Schools, who has been on Arlington county and school board committees.

The three who had applied earlier are: Michael E. Brunner, a former college professor now employed by U.S. Department of Agriculture, who has been active in McKinley Elementary School PTA and on school board study commissions; Barbara W. Cullicott, who works for the University of Virginia and has been active in Jamestown and Williamsburg PTAs, and has served on a school board committee; and Edna Earle Johnson, a lawyer who has taught government and served as a volunteer teaching English to Vietnamese refugees.