Virginia Del. Stephen E. Gordy won a Republican canvass in Fairfax County yesterday to become the GOP nominee in a special election July 15 to fill the Providence District seat on the Fairfax County Board of Supervisors.

Gordy, 66, a state legislator since 1983, defeated Robert W. Beers, a 38-year-old former aide to Supervisor Thomas M. Davis III (R-Mason).

The vote was 424 to 286.

Gordy will face Democrat Kate Hanley, a member of the county School Board, in the special election.

Hanley had no Democratic opponent.

"That was a big victory, really great," said Gordy, a retired Army colonel and public school principal. "I consider myself the underdog starting out" in the campaign.

Beers, who was running for elected office for the first time, conceded shortly after the polls at Marshall High School closed at 9 p.m.

Asked if Gordy was an underdog, county Republican Chairman James D. Swinson said: "I never admit to that."

He added: "We're going to run hard, we're going to run fair, we're going to put everything we have into winning."

The winner of the July 15 special election will replace Providence District Supervisor James M. Scott on the nine-member county board. Scott, a Democrat, announced earlier this month he would resign from the $21,589-a-year position June 3 to become director of community affairs for the Fairfax Hospital Association.

The seven-week campaign is likely to be hard-fought. Republicans now hold a 5-to-4 majority on the County Board, and a victory by Gordy would give them a 6-to-3 advantage and unquestioned dominance of policy making in the county.

Democrats say Hanley must win if they are to stand a realistic chance of regaining a majority on the county board in 1987, when all nine supervisors will stand for reelection.

The Republicans gained a majority on the County Board in November 1984 for the first time in a century.

Beers and Gordy differed little on the issues in Providence District, an irregular, elongated patch of land stretching from the Arlington border in the east to Fair Oaks Mall in the west with a population of about 85,000.

Each said, however, he had a better chance of defeating Hanley in the special election.

Beers had pointed out that if Gordy wins the special election, he will have to resign his seat in the House of Delegates, leaving the Republicans vulnerable to another strong Democratic candidate in yet another special election.

In his race for the House of Delegates last November, Gordy won reelection by just 98 votes over a relatively unknown Democrat, Jeff Fairfield. Officials of both parties said they were surprised by the closeness of the vote. In a newspaper poll in late 1984, Gordy was ranked 98th out of 100 state delegates in effectiveness.