Prince George's County Executive Parris Glendening consummated a deal with the county's state legislators yesterday in which he is promised state approval for a long-sought government center as the major project to emerge from his legislative agenda this year.

The agreement promised one victory for Glendening in Annapolis and restored an element of harmony to relations between him and the legislators that soured recently with rejection of a tax proposal that Glendening said would have raised $10 million for the county.

If the agreed-on deal goes through, Glendening will get General Assembly approval for $2 million in state start-up funds for the government center in Hyattsville and the county will sell $1.3 million in bonds to build a recreation center in Chillum.

The executive and his aides have been lobbying in Annapolis on behalf of the Hyattsville center since the legislative session began in January, providing tales of the inadequacy of the present County Services Building and information on a $27 million complex to be completed in 1989.

Eight legislators from the two election districts that would be serviced by the new recreation center agreed to support the administration's Hyattsville proposal and said they expect it to win House approval.

That prospect brightened considerably last night when funds for the government service center got preliminary approval from the House of Delegates and the recommendation of a Senate capital budget subcommittee.

"We needed to work with the county executive," said Del. Nathaniel Exum. "It's always good to have a chit."

"We might want a swimming pool next year," added Del. Sylvania Woods, smiling. Glendening and all the members of the county's legislative delegation are Democrats.

In order to win legislative support for the government center, Glendening had to overcome the objections of elected officials who feared that backing the Hyattsville project would cost them state bond money for their own pet projects. The executive also agreed to include $50,000 in the county bond sale to pay for the renovation of the Peace Cross site in Bladensburg.

Other state bond bills that received preliminary approval in Annapolis yesterday include $1.5 million to build a high technology institute in Laurel, $200,000 to renovate an unspecified black historic site and $200,000 to plan an indoor arena at the Prince George's Equestrian Center.

"We'd been working on the [Hyattsville project] for about two years," Glendening said. "At the same time, there are a number of other projects that came up that represented the top priorities of elected officials in individual districts."

Del. Timothy F. Maloney, who was highly critical of Glendening during the recent clash over the tax measure Glendening sought, was conciliatory. "I've got to commend Parris for being cooperative on the capital budget," he said. "If we could continue to cooperate on the operating budget, we could have a better time with our tax proposals."