Fairfax County unveiled details yesterday of a conceptual agreement with the developer of a new government center that calls for a larger complex costing about $13 million more than originally proposed.

Despite the increased cost, the agreement hammered out between the county and The Charles E. Smith Cos./The Artery Organization Partnership would permit the $83.4 million government center to be built using about $22 million less in tax-generated funds, according to Fairfax County Executive J. Hamilton Lambert.

Also, it would provide for "an improved road network in the entire area at minimal cost" to the county, Lambert said.

The agreement, which the Board of Supervisors voted 8 to 0 to send to public hearings in July, would increase the size of the center, to be built near I-66 and Rte. 50 in the Fair Oaks Mall area, by about 53,000 square feet over the size proposed when Smith/Artery was selected as the developer in September.

In another matter yesterday, the board voted to give Lambert a $10,000-a-year raise, bringing his annual salary to $108,000 and making him one of the few local government employes in the Washington area with a six-figure salary.

Negotiations between the county and Smith/Artery had been under way for about six months and reached a frantic pace last week as Lambert and Artery President Alan B. Geller exchanged a flurry of proposals and counterproposals.

The new agreement calls for Smith/Artery to build a 633,000- square-foot, $83.4 million complex in exchange for 116 acres next to the site and payments of about $24.6 million. Despite the bigger size and cost of the complex, however, only about $14.7 million would come from the county's general fund because alternative financing methods are to be used.

For instance, about $7.4 million would come from the sale of offices to county agencies that generate income, such as solid waste and sewer funds, while the county would offset about $8.5 million from the price tag by renting space in Smith/Artery buildings using state funds.

The September proposal called for Smith/Artery to build a 577,000-square-foot, $70 million complex in exchange for 116 acres and payments from the county of $5 million a year for 10 years. The developer plans to build 1.24 million square feet of office space and a 275-room hotel on 58 acres and a residential subdivision on the remaining land.

Critics, notably the Fairfax County Federation of Citizens Associations, blasted the September proposal, saying that the county was not getting its money's worth for the land, which is considered prime for commercial and residential development.

The 116 acres is part of a 183-acre tract purchased by the county for $4.1 million in 1979. With road and other improvements, it is worth about $42 million today, according to the proposed agreement.

In other actions, the board: Approved a secondary road improvement plan that calls for spending more than $130 million in state funds during the next six years, including $47 million for the Springfield Bypass and $11 million for the widening of Braddock Road.

Approved a 24 percent rate increase for county taxicabs, bringing the cost for one passenger to $1.20 for the first one-sixth of a mile and 20 cents for each additional one-sixth of a mile traveled.

Voted 8 to 0 to have a public hearing on a proposed zoning amendment that would restrict nude or seminude dancing to establishments that sell alcohol. No hearing date was set.