A Reagan insider with judicial experience today withdrew his name from consideration for the Supreme Court, and another well-informed administration official said the White House "was looking hard" for a woman to fill the vacancy caused by the resignation of Justice Potter Stewart.

"I've made it clear I don't want to be considered for the high court," said Deputy Secretary of State William P. Clark, who returned to Washington late Thursday after a two-week African trip.

Clark did not give a reason other than expressing a desire to return to his California ranch after completing his present job. But a high White House official said Clark is "badly needed" in his current post, where he has been a buffer between Reagan aides and the sometimes mercurial Secretary of State Alexander M. Haig Jr.

Clark was in Africa when Stewart's resignation was announced. He was mentioned immediately by White House insiders as one of three Reagan intimates who were potential candiates for the court.

The other two were White House counselor Edwin meese III, who withdrew his name on grounds that it was inappropriate for a presidential adviser to be considered, and Attorney General William French Smith, who said his name will not be on the list of recommendations for the court that he will submit to the president.

Clark served as Reagan's executive secretary when he was California governor, was appointed by Reagan to a trial court and then was elected for another term to the same court. Subsequently, Reagan appointed him to a state appellate court and then to the California Supreme Court.

An administration official said today that White House aide Elizabeth Hanford Dole, 44, wife of Senate Finance Committee Chairman Robert j. Dole (R-Kan), had emerged "high on the list" of people under consideration for the Stewart seat. She is one of a dozen nominees Smith is expected to submit to the president.

White House officials say Reagan will be guided by this list, but will not necessarily be bound by it. They also said the president could make his decision as early as mid-July.

"A woman is a good possibility," one well-placed official said.

Reagan promised in the campaign to name a woman to one of the first vacancies on the court during his administration. If he decides against picking Dole or some other woman, some in the administration think he will turn to Robert H. Bork, 54, the solicitor general in the Nixon administration. Bork is also understood to be on Smith's list.

After two days in Los Angeles and more telephone calls to southern Democrats on behalf of his economic legislation, Reagan flew to his ranch north of Santa Barbara, where he will spend the weekend. He is to return to Washington Sunday and fly to Denver for a speech to the NAACP Monday.

As usual, Reagan is expected to spend most of his weekend riding horses, clearing brush and chopping firewood.

On Saturday, Vice President Bush is to fly in to report on his just completed European trip. Bush will then meet reporters at Point mugu Naval Air Station before flying to Manila for the inauguration of Philippine President Ferdinand Marcos.