Fairfax City would have to pay Fairfax County $8.3 million a year to operate its schools next year under a proposed contract that would end a dispute over school costs between the two localities.

The proposed rate is $200,000 a year higher than under an old contract, which became the focus of elections in Fairfax City this spring. At that time the city supporters of a separate school system were saying that a new contract with the county would raise city taxes $1 million to $2 million.

Currently the county operates schools inside the city for 4,100 pupils.

Renewal of the city county negotiations began almost immediately after the city's May 2 city council election, in which Mayor Nathanial Young and all candidates who opposed continued cooperation with the county were soundly defeated. Young and the present council majority, who go out of office on Friday, had attempted to establish a separate city school system.

The proposed contract, which will be explained at city and county school board meetings tonight, must be approved by both county and city school boards, the City Council and County Board of Supervisors.

Approval of the contract by both sides appeared likely yesterday, although public hearings will stretch the approval process through the end of July. Although the appointed city school board could theoretically veto the contract, board president Richard A. Rucker, said yesterday the board "will execise its independent judgment" but will consider "the mandate" of the publid demonstrated in the city election. No county objections to the proposed contract were seen by county fiscals.

Its major provisions call for the small city of 21,000 and the surrounding county to drop all previous claims against each other - raised in more than a year of angry dispute over what the city's "fair share" of school costs should be - and establish new ground rules designed to improve city-county cooperation.

The increased costs to the city will come in two new school charges. One will reimburse the county for school services not offered directly at the city's seven schools but used by city students at county schools. The other is a general administrative charge for county handling and processing of all bills, salary checks and other financial matters. Present city school payments do not reimburse the county for such expenses.

Several small but hotly diputed issues also are settled under the proposed contract.

The city will now be credited with a pro rata share of federal and state grants received by the county (amounting to $239,000 this fiscal year., no longer will the city pay both rental and capital replacement costs on the 17 county school buses it uses but the annual rental charge it pays will rise from $500 a bus to $1,500.

City Councilman Lee H. Wigren who headed the city's negotiating team, praised the contract as fair "and on the balance an affordable one that keeps us if an excellent county school system."

However, Young criticized it as a "bad deal" for the city and insisted that "no contract's a good contract" that keeps the city within the county system. Young also disputed the figures released at yesterday's press conference by Wigren and the city negotiators. He claimed the actual cost to the city will be about $800,000 more a year not $200,000 under the proposed contract.