A bitter four-year dispute between the Metro transit authority and a labor union representing more than 500 white-collar workers appears to be drawing to a close in the wake of a U.S. Court of Appeals decision upholding the union's key allegations.

The transit agency has agreed to furnish back pay, estimated at $650,000 to $750,000, to about 200 union members found by a federal judge to have been improperly denied pay raises. Metro has dropped its threats to fire union activists and said it will soon start contract negotiations with the union.

Jim Sheridan, president of Local 2 of the Office and Professional Employees International Union, hailed the rulings and Metro's actions as a victory for the union, which represents clerical workers, accountants, engineers, lawyers, planners and other professional employes.

According to Metro officials, the union members' current salaries range from $10,000 to $50,000 a year.

"The courts have told the authority to do what they should have been doing," Sheridan said.

Carmen Turner, Metro's acting general manager, said the transit authority would begin negotiations as soon as possible and added, "I will be pleased to see this matter settled."

The impending round of labor negotiations raises prospects of further financial pressures for Metro officials, who are seeking to restrain the transit system's soaring multimillion-dollar deficits.

The transit authority also has been embroiled in several other labor conflicts, including protracted contract talks with Local 689 of the Amalgamated Transit Union, which represents nearly 5,500 bus drivers, subway operators, mechanics and other workers.

These negotiations are expected to set a pattern for contract talks with a Teamsters local representing Metro bus employes in Prince George's County.

In addition, Metro has been engaged in a prolonged dispute with another Teamsters local representing about 200 transit police. Metro's board of directors, which previously rejected a proposed agreement with the union, voted yesterday to accept a revised accord.

Terms of the tentative contract, which has not been ratified by Local 246's members, were not disclosed.

Arlington County Board Vice Chairman John G. Milliken, who heads a special cost-containment committee established by Metro's board of directors, described the prospective negotiations with the office and professional employes' local as "obviously a complicating factor" in cost-cutting efforts. "It's another constraint on what you can do," he said.

Local 2 had sued the transit authority, charging that it engaged in "unlawful retaliation" by denying two annual pay increases to union members. It also accused Metro of a "malicious violation" of a previous arbitration decision by refusing to bargain with the union, which was elected to represent Metro employes in January 1981.

One controversial issue in the suit centered on a December 1981 letter written by former Metro general manager Richard S. Page in which he warned about 300 employes "to stop all involvement" in Local 2. He added that "failure to do so may result in your termination." Among the employes threatened with possible dismissal were 10 of the union bargaining committees' 12 members.

Last November, U.S. District Court Judge Barrington D. Parker endorsed the union's complaints, ordering the back pay awards and recognition of the union. A three-judge Court of Appeals panel upheld his decision earlier this month.

Considerable uncertainty still surrounds the prospective contract negotiations between Local 2 and Metro, partly because several issues are pending in court. The Court of Appeals has not yet handed down a full opinion spelling out its reasons for upholding Parker's ruling.

William J. Curtin, a lawyer representing Metro, said that until the appellate court's opinion is issued, the transit authority could not rule out a possible request for a rehearing or an appeal to the U.S. Supreme Court. Nevertheless, Curtin said, Metro officials are prepared "some time this summer to sit down and start bargaining."

Local 2 president Sheridan said the union will press for higher salaries, cost-of-living adjustments tied to the Consumer Price Index, a broadening of overtime pay and a wide range of other changes. Similar demands by other unions have been opposed by Metro officials.