Hedley Donovan, a senior adviser to President Carter whose duties were a mystery even to many of his colleagues in the White House, has resigned effective Aug. 15, the White House announced yesterday.

Donovan, 66, the retired editor-in-chief of Time magazine, joined the White House staff last summer in the midst of the president's shakeup of the Cabinet and his senior staff. His appointment was cited at the time as evidence that after 2 1/2 years in office Carter was reaching beyond his tightly knit band of senior aides from Georgia for a broader spectrum of advice.

Donovan, who served without pay, was given free rein to advise Carter on both foreign policy and domestic issues and was promised direct access to the president. However, after a year in the job, the only project with which Donovan was visibly associated was the creation of the President's Commission for a National Agenda for the Eighties.

The 50-member commission of prominent Americans is now at work with the help of a staff of 30 and a $2.8 million budget.

White House press secretary Jody Pwell said yesterday Donovan also was involved in another project for the president, which he declined to identify. Powell said Donovan had always planned to serve only for about a year. He said he did not know if a successor would be named, adding that it is unlikely a replacement will be appointed during the upcoming "political season."

It is not clear how much or on what subjects Donovan advised Carter. His meetings with the president were included on Carter's public schedule, which was unusual because most senior aides see the president regularly without any public notice.

Some White House aides believe Donovan's lack of specific duties and powers may have handicapped him in the role of senior adviser. His position was sometimes contrasted with that of White House counsel Lloyd N. Cutler, another experienced figure whom the outside who joined Carter's senior staff at about the same time.

Cutler's responsibilities as counsel involved him in a number of high-priority missions, increasing his influence within the White House.

Cutler headed the White House's Moscow Olympics boycott effort and was deeply involved in aspects of the Iran hostage crisis and the controversy over Billy Carter's ties to Libya.

In the White House announcement of the resignation, Donovan noted that he will be leaving the White House staff after one year and, having completed the assignments given him by Carter, wished to return to the New York area for "personal reasons."

The announcement quoted Donovan as thanking the president for "a most interesting year, made especialy pleasant by your own thoughtfulness and good humor, and the warm hospitality you and Rosalynn have shown me."

In reply, according to the announcement, Carter praised Donovan's "sound judgment and advice" and said, "You have been very helpful to me and to our White House deliberations during some important and trying times for our nation."