Prince George's County Executive Parris Glendening, faced with the expiration next June of virtually all county labor contracts, appointed a Baltimore lawyer yesterday as the county's chief labor negotiator and announced his intention to create an office of labor relations.

The new office will oversee both contract negotiations and routine administration and, said Glendening, signals his intention to forge a more cooperative relationship with labor than existed under his predecessor, Republican Lawrence J. Hogan.

" . . . The confrontation of the last several years has ended," said Glendening, a Democrat, of an era that included a 1980 strike by county employes culminating in the firing of 37 jail guards. Recently a circuit court judge ordered all the guards reinstated, at a projected cost to the county of about $1.3 million.

The new appointee is Frank W. Stegman, 36, a former partner in the Baltimore law firm of Gebhart and Smith, where he specialized in the management side of labor relations. Stegman will be under contract to the county for a fee of $25 an hour (to a limit of $30,000) until legislation establishing the new office goes into effect. Stegman will then head the new labor office as the county labor commissioner, for a salary as yet undetermined.

Union leaders contacted yesterday enthusiastically endorsed both the creation of the new office and the appointment of Stegman, whom many met Monday. They said the office would allow more consistent communication with county officials on a daily basis. The leaders also praised Stegman for his reputation for fairness.

Former county executive Lawrence J. Hogan employed the services of a Washington law firm of Arent, Fox, Kintner, Plotkin and Kahn to perform most labor negotiations, aided by county employes. It was an approach that virtually all labor leaders and many county personnel specialists criticized. Union leaders complained the lawyers could not bargain effectively since they did not have a close relationship with the executive and that they had little understanding of county government or sympathy for county workers' concerns.

Moreover, said Fraternal Order of Police President Mahlron Curran, many workers resented the large fees paid to the law firm. According to Glendening, the county's firm's chief negotiator, Allan Siegel was paid $100 an hour for his work for the county, and fees paid to the firm totaled $200,665 between 1979 and 1982.

Glendening said the creation of the new office was recommended by one of the citizen task forces he formed soon after his election.