A former reporter for the Loudoun Times-Mirror was elected by the Loundoun County Board of Supervisors yesterday to fill the unexpired term of the Sterling District board member, who resigned last month.

Shannon Geddie, 38, a Democrat, was nominated by the board at a workshop Friday and was sworn in yesterday. She replaces George Yeager, former board chairman, who resigned to accept a promotion with the Columbia Gas Co. in Charleston, W.Va.

Broad Run Magisterial District Supervisor Carl F. Henrickson, a Democrat, was elected by a 5 to 3 vote to serve out Yeager's term as board chairman.His opponent, Henry C. Stowers (D-Dulles), remained in his position as vice chairman.

Geddie is a graduate of the University of Texas and is a native of San Antonio, Tex. She has lived in the area about six years and has worked at the Loundoun TImes-Mirror for about two years.

Yeager left his position on July 11. If the vacancy had occurred before that date a special election would have been required in November to fill the seat.

Republicans had called on Yeager to step down in time for an election, but Yeager refused, saying that it would require a candidate to run in November, again in the spring primary and again in November 1979 in the general state election.