The leaders of a special Senate subcommittee created to investigate Billy Carter's activities as a foreign agent are considering appointment of a prestigious lawyer to direct the inquiry.

A spokesman for Sen. Birch Bayh (D-Ind.), the subcommittee chairman, said yesterday that Bayh would like to hire someone "who had experience in this type of thing and who has no ties to either party." Sen. Strom Thurmond (R-S.C.), the vice chairman of the panel, was also said to be enthusiastic about the idea.

The subcommittee is expected to discuss the course of the investigation at a meeting Thursday. The session was to have been held this morning, but it was postponed to allow more time for the preparation of a preliminary staff report and for further discussions between Bayh and Thurmond.

The delay makes it even more unlikely that the subcommittee will be able to make much headway before the opening of the Democratic National Convention in New York City Aug. 11. Preliminary staff interviews of White House and Justice Department officials about their contacts with the president's brother have yet to begin.

President Carter has pledged to cooperate fully with the inquiry, which the Senate voted to initiate last week after Billy Carter disclosed that he had been paid $220,000 this year by the Libyan government. He registered as a foreign agent for the Libyans July 14, saying later that he did so to avoid a criminal investigation of his activities.

A resolution of inquiry, seeking all pertinent records in the case, is also pending before the House Judiciary and Foreign affairs committees. Justice Department officials are expected to submit some documents to those committees today.

Some of the president's advisers are urging him to announce his willingness -- even eagerness -- to testify before the Senate subcommittee in open session, but also to ask that his appearance come before the start of the Democratic convention.

White House press secretary Jody Powell said, however, that no decision has been made on just how the president will respond to the panel's questions. The possibility of written responses to formal interrogatories has also been suggested.

Senate sources said the subcommittee would be ill-prepared to question the president thoroughly at this point, but would find it difficult to turn aside any offer on his part to testify in person.

"Politically, it would be a smart thing for him to do," one source said.

Only seven members of the subcommittee, all from the Senate Judiciary Committee, have been named thus far. Two other appointments from the ranks of the Senate Foreign Relations Committee remain to be made. f