The Senate yesterday confirmed the nomination of Chief Judge Harold H. Greene of the D.C. Superior Court to the U.S. District Court here and thus formally opened up competition for the highest post in the local trial court.

Greene's successor, who will preside over 43 judges and close to 1,000 support personnel who work in the new, $40 million District of Columbia Courthouse, will be designated by the D.C. Judicial Nomination Commission.

The commission, in anticipation of Senate confirmation of Greene's nomination, has interviewed four judges on the Superior Court for the chief judgeship, various sources have said.

The four judges interviewed were James A. Belson, Joyce Hens Green, H. Carl Moultrie I and Tim Murphy, sources have said.

Up to now, consideration of selection of a new chief judge - as well as the lobbying within legal circles that usually accompanies that process - has remained low key. With the Senate's confirmation of Greene yesterday, however, the nomination commission is expected to move the selection procedure into full swing.

Commission chairman Charles Duncan said yesterday that the panel has scheduled a meeting for Saturday morning, at which time the selection of a new chief judge will be discussed. Greene, in a telephone interview, said last night that he will not resign from the Superior Court for at least a couple of weeks.

Courthouse observers generally agree that a principal factor in selecting a chief judge is the candidate's ability to be an effective administrator in the high volume city court system. In addition to mastering mechanics of the court's operation, the chief judge of the Superior Court is also the main lobbyist for the trial court in both the city and federal governments.

Of the four reported candidate's for Greene's job, Belson and Moultrie are considered the leading contendors, according to sources.

Belson, who has been on the local bench since 1968, has often handled complicated civil cases. Moultrie, a Superior Court judge since 1972, frequently sits in the court's felony division, hearing serious criminal cases. Green presided over a recent series of complicated tax trials involving the city government. She has been on the Superior Court bench since 1968. Murphy, appointed a judge in 1966, also frequently hears criminal matters and participates in research projects about court operations.