Once upon a time, in the happy springtime of the Reagan administration, the White House staff was the pervasive domain of an all-powerful, three-man operation known variously as the Trio, the Triumvirate or the Troika.

From their daily breakfast each morning in the office of chief of staff James A. Baker III until their last late afternoon meeting after President Reagan had retired to the White House residence, the trio of counselor Edwin Meese III, deputy chief of staff Michael K. Deaver and Baker defined, guided and carried out presidential policy.

The Trio is still around these days, but its harmony has been shattered. Its dominance has been diminished by the addition to the White House staff of another influential, longtime Reagan intimate, national security adviser William P. Clark. And its influence has been reduced both by the rise of lesser aides and the increasing proclivity of the president to do what he wants to do, no matter what his staff is telling him.

During a recent 10-day period in the White House, Meese came under internal criticism for purported "leaks" of foreign policy information, Deaver received a rare personal reprimand from the president for premature disclosure that Reagan would address a joint session of the British Parliament and Baker was attacked by conservatives for advocating compromises on the president's economic program.

Nonetheless, the Trio continues to rule the roost at the White House when it comes to determining daily activity. Decisions reached at the breakfasts in Baker's office are communicated at the daily senior staff meetings that follow. These meetings, once important, have largely been reduced to a convenient forum for issuing marching orders. In the changing fortunes of the top White House advisers, Meese is the most obvious loser. The rise of Clark has virtually removed him from the process of foreign policy decision making. Many of the longtime California associates Meese brought with him to the White House have resigned, been pushed aside or shunted into jobs with little influence.

Some aides predict, however, that the change in Meese's status ultimately could increase his influence. Senior White House officials say that Meese has been relieved of doing what he does not do well, which is to manage, and freed to concentrate on what he does best, which is to counsel the president.

"My role has been reduced to what it was intended to be in the first place," Meese said in a recent interview.

Other changes have emerged in a White House staff that increasingly feels the pressures and strains arising from growing discontent with Reagan policies in the Congress and the country. This is how high administration officials describe the power balance within the White House today:

* Clark, though not a member of the Trio, has emerged as a powerful personal adviser to the president and the fulcrum of his foreign policy. One aide describes him as "the proverbial 600-pound gorilla that everyone has to pay attention to" and another observes that fellow Californians Meese and Deaver are inevitably deferential to him in meetings. Officially, Clark's mandate is limited to foreign policy. Unofficially, Reagan is likely to ask his opinion about anything.

* Two lesser-known aides, presidential assistant Richard G. Darman and Cabinet secretary Craig L. Fuller, play an increasingly important role in the White House. Darman is the funnel for the flow of paperwork going to the president and coming back from him; Fuller is the White House link to Reagan's Cabinet. One or both attend most White House meetings.

* It is an open secret in the White House that Meese and Deaver don't get along even though they continue to work together formally. One well-placed White House official said the personal relationship between Baker and Deaver also has become cooler. And other aides say that the Trio, particularly Baker, are showing increasing signs of fatigue.

* Baker is the first among equals of the triumvirate, demonstrating an old White House axiom that "whoever controls the staff controls the White House." Reagan tends to listen to him on personnel issues. But Baker is described as increasingly isolated from the president on issues of substance and he is under attack from various conservatives for purportedly being closer to Vice President Bush than to Reagan.

* Bush, who lunches privately with Reagan every week, has become a behind-the-scenes presence in some White House decisions. The vice president is believed to be more influential with Reagan on foreign policy issues than domestic. But Reagan also consults him on personnel issues when the Trio is in disagreement. Last November, when Meese and Deaver recommended the dismissal of budget director David A. Stockman and Baker urged his retention, Reagan asked Bush his opinion. Bush spoke up for Stockman, whom Reagan kept on.

Though Alexander M. Haig Jr., the sensitive secretary of state, continues to view Bush warily, it is Clark, Haig's former deputy, who holds the keys to administration foreign policy.

"He has brought foreign policy back to the White House," says a well-placed administration official. "He is the fulcrum."

Baker has achieved a respectful, though arms-length working relationship with Clark, whom the chief of staff calls "an effective synthesizer of the national security process."

Clark's influence with Reagan is the product of their close relationship in Sacramento. When Gov. Reagan's office was in turmoil in 1967, Clark took over as executive secretary and established a harmonious, team-style leadership that became the pattern for the White House trio. A soft-spoken 50-year-old California rancher who shares Reagan's fondness for horseback riding, Clark is also well-liked by Nancy Reagan.

He also is a longtime friend of Secretary of Defense Caspar W. Weinberger, who was Reagan's director of finance in California when Clark was executive secretary. But some White House officials predict that Clark may have more long-term difficulty with Weinberger, who has long enjoyed his own access to Reagan, than with Haig, who remains an outsider to the Californians.

Clark's style, which is low-key and friendly but decisive, has had a noticeable impact within both the National Security Council and the White House. He has replaced a number of staff members, some of whom Clark referred to as "ideologues" at NSC. A White House official said that Clark also has asserted his--and the president's--authority in dealing with both Weinberger and Haig.

"He doesn't bluster, but he is insistent," said one aide. "If he's not getting something he needs from State or Defense, he will say to Cap or Al that an item is being presented to the president at 9:30 the next morning, and that if they want to have input they'd better get the material to the White House in a hurry. They get the point."

On the first morning Clark was in the White House after he replaced Richard V. Allen as national security adviser, Meese set a chair for Clark in his morning management meeting and asked him to review the NSC briefing. Clark declined.

"I'll be reviewing that with the president," he said.

Reagan underscored his confidence in Clark by walking with him outside the Oval Office at prearranged White House "photo opportunities." Clark successfully prompted Reagan to speed up his selection of a new chairman of the Joint Chief of Staffs. After the president chose Army Gen. John W. Vessey Jr., Clark pushed him to announce it immediately, pointing out that the decision would probably "leak" if he withheld the announcement.

Clark's influence is enhanced because of his friendship with Deaver, who remains the aide with the closest personal ties to the president. Deaver, who has given up his business and spent much of his life savings during his 15 months in Washington, wants to leave at the end of the year for personal reasons. His White House colleagues are betting that he won't.

"He holds the harness, and he isn't going to be leaving the White House," says one aide. "The Reagans won't let him leave."

Another aide calls Deaver a "good arranger of the balance of power." He is a careful student of both the president's and Nancy Reagan's moods and preferences. Others in the White House defer to him on questions of timing and procedure.

"If we have to tell the president some bad news, Mike is far and away everyone's first candidate to tell him," says a White House official.

A sign of Deaver's influence is that he recently prevailed over Haig in the selection of an assistant secretary of state for international affairs--a job that in most administrations would be routinely chosen by the secretary of state. Deaver's involvement was another sign of the personality politics that often prevail within the Reagan administration and demonstrated again that Haig remains an outsider.

Still, White House officials predict that Haig and such other controversial figures as Stockman and Interior Secretary James G. Watt will remain in the Reagan administration through the 1982 elections despite recurrent rumors that one or more of them will leave. They also anticipate that all of the important players in the White House will remain on the team.

"There are no changes contemplated in the Cabinet or upper levels of the White House," Baker said last week, making it clear he was talking about the 7 1/2 months between now and the off-year elections.

One of the rumored departures is Baker himself, perhaps to a spot in the Reagan Cabinet after the election. Some speculate that Baker ultimately could replace William French Smith as attorney general, to which Baker responds: "I am enjoying serving this president. I serve at his pleasure and I am going to do whatever he wants me to do."

There has also been speculation that Meese will soon depart possibly, once again, for the attorney general's job, or a seat on the Supreme Court. Meese, however, has publicly denied this.

The talk of changes is a sign of the present restlessness in the high levels of the Reagan administration during the traditionally difficult second year of a presidency. The restlessness is compounded in this White House by the constant sniping from the right wing of the Reagan constituency at Baker and other members of the staff who worked for other Republicans before Reagan.

One favorite target is Darman, who is forever tarnished in the eyes of the right by his onetime service to Elliot Richardson. By most accounts, Darman is one of the most influential White House aides, even though he is less well-known outside than any member of the Trio. The rules of the White House staff game are that no paper can go to the president without Darman seeing it first, a procedure that prevents any member of the Trio from making an end run around the others.

Darman, with Deaver's encouragement, has sought to reduce the paper flow to the president to keep him from being inundated with detail. Recently, he held back clippings on federalism that were presented for presidential perusal by Rich Williamson, the White House assistant for intergovernmental relations.

Instead of sending in the clippings, Darman attached a note saying that they were available should the president want to see them.

Fuller's influence also has grown. He coordinates meetings of Cabinet members and the president, representing Cabinet interests to the White House and vice versa. He also has begun to speak out more.

For example, Fuller spoke up at a Feb. 22 meeting with Reagan and suggested that it would be best for the president to wait on decontrol of natural gas. Reagan went along.

But there are other times when the president chooses not to follow the recommendations of any of his top advisers. No matter how well the information flow functions, there are times when Reagan ignores or overrules even the best-constructed recommendations of his staff.

Indeed, in a White House that is relatively open about the processes by which information reaches the president, a mystery persists about the way Reagan reaches his own decisions on many substantive issues.

"Whatever else you can say about him," said a top aide recently, "Ronald Reagan is not the captive of the institutional presidency. We've got a good system for decision-making, but he can be a majority of one."