It was almost a typical victory party scene. A reporter called the Prince George's police union headquarters two weeks ago to get the results of the vote on a hard-fought contract, and a jubilant fellow answered the phone.

"What's happening to the contract?" the reporter asked.

"It's gone. History," said the man on the other end, straining to be heard above the din of celebration. "We rammed that baby through and I'm going partying. You better believe it."

The scene was typical except that the voice belonged to Frank W. Stegman, the new county labor negotiator who had bargained management's side of the police officers' new contract. And labor leaders were happy with him despite the fact that, although the contract offered the county's 850 police better pension benefits and some job security, it contained no cost-of-living increase for the first time in 10 years of collective bargaining.

According to labor leaders and county officials, Stegman's presence at the Fraternal Order of Police headquarters the night of the vote and at a celebration with the FOP's president afterwards is a symbol of a government open to a more cooperative era of labor relations in Prince George's, where a long history of hostility between the government and its workers has included strikes and numerous grievance complaints filed with the Personnel Board.

Stegman, a curly-haired, jocular graduate of the Georgetown University Law Center, has been a key figure in the county's success so far, they say.

"Negotiations were handled in a very professional manner . . . in a fair and equitable atmosphere," said Fraternal Order of Police president Mahlron Curran the day after the vote.

"I think he Stegman is a refreshing change," said former FOP president Laney Hester, who added he "wouldn't let previous negotiator Allen Siegel in the door."

Stegman, 37, was hired by Prince George's County Executive Parris Glendening last December to head a new Office of Labor Relations, responsible for contracts with the county's dozen union locals and for adminstering day-to-day labor problems. Glendening, a Democrat who was elected with strong labor support last fall, said he took the idea from a citizen task force he appointed to help him with his transition.

The task force criticized the approach of the previous executive, Republican Lawrence J. Hogan, who employed the services of a management-oriented Washington law firm to bargain with county unions.

The task force charged that the government had failed to provide employes with a method for resolving individual and relatively minor disputes without a confrontation before the county Personnel Board or in court.

Union leaders also accused Siegel, the firm's chief negotiator, of insensitivity to their concerns and resented his $100-an-hour fees, which cost the county $200,665 between 1979 and 1982, according to Glendening. They also objected to Siegel's inability to seal agreements at the bargaining table, a result of Hogan's insistence that he personally approve all details.

Glendening said he appointed Stegman to the new post, which is expected to pay between $56,000 and $59,000 a year when approved by the County Council, because he wanted someone with the attitude "that I'm going to do a good professional job, but I'm not your enemy." Glendening has given Stegman authority to approve the details of all contracts he negotiates.

In the five months since his appointment, Stegman has helped Glendening fulfill a campaign promise to implement a 1980 contract that Hogan had refused to sign, despite a court order, ending the county's longest running labor dispute.

In a county in which negotiations have continued for as long as 18 months after contracts expired, Stegman completed negotiations with two of the county's largest unions, the police officers and firefighters, before their June 30 expiration dates--and without either side's resorting to binding arbitration, a right those unions won in 1980.

In addition to his work with the contracts, he has earned high marks for a willingness to familiarize himself with employes' working conditions and problems and for being consistent on economic issues.

"He listens," said Carolyn Larkin, president of the union that represents the about 600 staff nurses at the county's three hospitals. "He's really good at trying to get at the heart of matters. He's certainly not giving things away, but at the same time he's trying to address the professional issues which concern us."

Stegman, who lives in Howard County, said he likes his work because "the jobs of the police and the firefighters are better because of what we did." Because the county lacked the resources to provide raises, he said--"and let's face it, you can seal any deal with dough--the job required a little more creativity."

One improvement in the police contract, for example, simply required printing more copies of the pension plan so that each union member could have a copy to study.

Stegman was raised in the small town of Sycamore, Ill., where he insists that his chief pursuits were part-time construction jobs, drinking beer and football. He was elected to two honor societies when he attended the University of Arizona.

He spent seven years as an associate at Morgan, Lewis and Bockius, a nationally known labor firm that represents corporations in labor disputes, yet he maintains a casual appearance, strolling the halls of the county building in shirtsleeves and propping his feet up on his desk during a conversation. He is likely to confirm an appointment by saying, "Hey! Be there or be square!"

But Stegman's casual demeanor masks a tough, competitive inner core, said friend and fellow lawyer Robert Dormer.

"When he's working on something, you can't speak to him until he's finished; it could be days," Dormer said.

Stegman says that originally he wanted to represent the union side of labor law, but he switched when he took a part-time job with Morgan, Lewis and Bockius during law school and realized that "it takes reasonable people on both sides to make anything work."