The long-simmering dispute over whether Fairfax City continues to contract with Fairfax county to operate city schools appears to be about over - for this year at least.

The city school board will hold a public hearing Monday night and the newly elected City Council will hold a similar hearing at its first meeting Tuesday night to consider and vote on the proposed new school contract.

The new agreement, if approved as expected, will cost the city about $200,000 more than the $8.1 million the city was due to pay Fairfax County under the existing contract - cancelled last fall at the height of the city-county feud over just what is a fair amount for the city to pay to have the county operate its seven schools and teach its 4,100 students. The city has a population of 21,000.

Approval of new contracts for other county services to the city, including sewer, trash collection, libraries and health services, are expected to be negotiated quickly if the thorny school issue is settled. The contracts would be signed at one time and must be approved by both city and county school boards as well as the City Council and county Board of Supervisors. Few county objections to the contracts are anticipated.

The $200,000. or 2.5 percent, increas in what the city would pay for schools is far below the $1 million to 2 million increase that proponents of a separate city school system were predicting last fall. Advocates of a separate Fairfax 1961 when Fairfax became independent of the surrounding county, made money a major issue in the school dispute.

The latest estimate of running a separate city school system was made in a $50,000 study released last week but ordered before the May 2 election by the defeated majority on the City Council - who put the city on a separate school council members all endorsed keeping Fairfax City schools in the county system.

The new study does not appear to support the argument that the city can do it cheaper. It found what previous less-expensive studies have found - that it would cost the city at least as much or more to run its own schools. The consultants estimate the city would need to spend $8.7 million in fiscal 1980 to operate an independent city system with schools equal to those the county now provides - plus $1.1 million in additional "start-up" costs this coming school year.

This is about $370,000 more expensive than the $8.3 million the city would pay Fairfax County during the coming school year under the proposed new contract. But the figures are for different years and it's not known how much more the county will ask to run city schools next year or whether an estimate for an independent school system might not also be higher next year.

The proposed new contract not only sets the amount the city would pay but also settles numerous small issues that have caused friction between the two Fairfaxes for more than a year since contract negotiations began in March 1977.

First it creates a "perpetual" school contract and calls for a three-year notification before either the city or county can cancel it, compared to the present 18-month notice invoked last fall when the current contract was abruptly cancelled by the county. This would give the city more time to set up its own school system if it decides to do so in the future.

It simply drops all past financial claims the city and county made against each other over school costs and agrees that the county will credit the city with a pro-rata share of federal and state school grants the county receives, something not done in the past and which would give the city a $240,000 credit for this year alone.

It also adds a new tuition charge the city would pay to help cover county administrative costs in running city schools and costs for providing school services in addition to that offered at the seven city schools - costs the city presently is not charged for They are estimated at $217,000 for next year.

The contract also extends the terms for the city to buy the four schools in Fairfax still owned by the county. The city has been in the process of buying the schools to cut down on school rental charges. The county has agreed to let the city buy the remaining buildings at the 1965 contract price, although it previously insisted the city pay current fair market value for them at least an additional $1.75 million, the county estimated.

The agreement also would guarantee city specific consultation right before the county school board mases decision aftecting schools within the city, including such things as boundary changes, school closings, selection of principals, use of schools for non school activities and citizen participation on advisory groups.

It also would guarantee at least one formal annual school board meeting with the county and provides for a three-month annual review period of "safety value" which the negotiation committee said the in the future "will aid in resolving . . . differences before they become major issues.