Since President Reagan replaced Alexander M. Haig Jr. with George P. Shultz last July, the new secretary of state has enjoyed an influence and authority far greater than Haig was able to achieve in his self-described role as "the vicar" of U.S. foreign policy.

To the public at large, Shultz has seemed almost invisible as he has burrowed himself into a collegial approach to decision-making favored by the White House. Even among people who closely follow foreign policy-making, he remains largely an enigma, known primarily for his low-key and pleasant manner, instinct for compromise, solicitation of a broad range of opinion on every issue and disconcerting habit of listening a lot but saying little.

Yet Shultz has been the principal force in profoundly changing the thrust of U.S. policy in four areas the administration considers top priorities:

* The Middle East. In his first major move, Shultz last summer was chief architect of the presidential initiative in which Reagan shook off a year and a half of inaction and put his name and prestige on a new attempt to achieve a comprehensive settlement of the Arab-Israeli conflict.

* U.S.-West European relations. Through persistent, quiet diplomacy, Shultz defused, at least temporarily, the threat to Atlantic Alliance unity caused by angry European rebellion against the administration's sanctions on suppliers to the Soviet natural gas pipeline project.

* Central America. Without abandoning the administration's determination to combat leftist guerrillas and communist influence in the region, Shultz took much of the heat out of this controversial policy by dropping the hard-line, rhetorical threats employed by Haig and opting instead for quiet cooperation with the democratic governments of the area.

* International economic relations. Shultz, who describes himself as "an economist and labor relations mediator" and who held three economic Cabinet posts in the Nixon administration, has pushed harder than any secretary of state in recent memory to make an assault on global economic ills a major focus of U.S. policy.

In the process, Reagan, who took office with an attitude verging on open hostility toward foreign economic aid and multinational lending institutions, lately has shifted his rhetoric toward an almost ardent championing of the need for greater international cooperation to help countries such as Brazil, Mexico and Argentina overcome debt problems.

In all of these areas, policy approaches adopted since the summer are still in their infancy, and some time must pass before a determination of whether they are succeeding.

Concerns are already being raised about whether the Mideast initiative is becoming bogged down in inertia, about whether the dropping of the sanction against the Soviet gas pipeline will lead to improved U.S.-European cooperation on East-West trade and whether U.S. efforts to exert leadership in the economic sphere are too little and too late.

Still the fact that these approaches are being tried--that Reagan could drop his chairman-of-the-board image to involve himself in the labyrinthine passions of the Middle East, that he could be flexible enough to modify his stubbornness about the pipeline and suspicion of organizations such as the International Monetary Fund and World Bank--is a significant commentary on how much administration policy has changed in six months.

There are many reasons for the changes. As one senior State Department official noted, "In most of these cases, the administration found itself facing a situation that was on the verge of explosion and that couldn't be ignored. More than any individual, it was the circumstances of the moment that impelled the change."

But the same official acknowledged, "Insofar as you can say a particular person was the main force in steering decisions along a specific path, it was Shultz. The president is comfortable with George as he never was with Haig. He trusts his judgment, and George in turn is very careful to explore every option, to look at them not as his policies but as things that the president will have to live with and, when he recommends a specific course, to be sure that the president is aware of its dangers and weak points as well as its virtues.

"When Shultz says, 'I think this is the way we should go,' you can be sure he's picked the course that he thinks best meets the tests of fairness, practical compromise acceptable to all the parties and consistency with the president's wishes and convictions."

In short, Shultz has proved adept at working closely with the president without touching off jealousies and turf rivalries that plagued his predecessor. More importantly, he has also shown that, when confronted with problems requiring immediate attention, he can use skills acquired in his years as a labor mediator to defuse them and ward off threat of immediate danger.

Less clear at this stage, however, is a sense of whether he can move from one-on-one problem-solving to fashioning a grand design that will rescue the administration from the erratic, tension-provoking fits and starts that characterized foreign policy in the first year and a half of Reagan's tenure. Compounding the lack of clarity on that score has been a certain amount of confusion about Shultz's political and philosophical colors.

To many uncomfortable with the hard-line dogmatism of the Reagan administration, the policy changes have come as a pleasant surprise. Some liberals have even tended to regard Shultz as a sort of covert kindred spirit burrowed into the government and working to modify the president's course.

Lately, though, that attitude has undergone revision, largely as the result of disappointment over the administration's failure to seize on the accession of Yuri V. Andropov to the Soviet leadership and seek to ease severe East-West tensions by testing new approaches to arms control and other aspects of U.S.-Soviet cooperation.

Those who saw the death of Soviet president Leonid I. Brezhnev as an opportunity for bold policy departures had looked to Shultz to provide the leadership. However, they were sorely disappointed when the secretary, at a news conference shortly after his return from the Brezhnev funeral, spoke in uncharacteristically tough terms of the "martial music" he had heard in Moscow and made clear there would be no major change from tough and wary Cold War attitudes maintained toward the Soviet Union.

That led some of Shultz's liberal admirers to reassess hopes that he would provide innovative directions across the broad spectrum of foreign policy and to conclude instead that he is essentially a "man who goes along to get along."

However, that assessment was disputed by one of Shultz's key State Department aides who insisted, "It is simply incorrect to assume that George took the party line on the Soviet Union because it was the safe or politic thing."

The official added, "George feels strongly that there's no big dramatic thing we can do, that the wiser course is to show patience and approach Soviet relations cautiously over time with lots of bits and bites. He believes that it's important not to become compulsive about the idea that we have to do something vis-a-vis the Soviets simply because they're there.

"That may disappoint some people as a conservative attitude," the official concluded, "but the reality is that Shultz starts as a conservative. He's not a liberal. He's a conservative, and that's the key to understanding what he's all about."

The point is accurate but fails to specify where Shultz fits amid various streams of conservatism in the Republican Party. Certainly he stands miles apart from the New Right coalition of Sun Belt ideologues, neoconservative defectors from liberalism and Moral Majority adherents who form the hard core of Reagan's support. Nor is he at home in the more traditional Republican conservative wing based in the midwestern heartland and reflecting frequently insular interests of that region's business and agricultural constituencies.

Instead, people who know him well agree that Shultz is more in the mold of the so-called "Eastern establishment Republicans" whose strength derives from ties to the great banks, law firms and academic institutions of the East Coast and who, in modern times, have looked for leadership to figures such as Thomas E. Dewey and Dwight D. Eisenhower.

For more than a century, they have made frequent alliances with Republican progressives to form the party's independent Mugwump tradition. And, they differ markedly from other conservative factions in their more pragmatic willingness to concede the need for flexibility in adjusting to changing times, their internationalist outlook, their interest in making government function in an efficient, corruption-free manner and their passion for reform and respect for personal liberties.

Shultz was picked for the job, in large part, because of his credentials as an internationalist well within the mainstream of postwar establishment thinking.

Reagan was aware that, except for Henry A. Kissinger, no other prominent Republican had sufficient stature among the European allies to overcome their fear that Haig's departure signaled a retreat into isolationism or an extremist view of U.S. power and responsibilities.

Since then, Shultz's decisions and approaches have consistently echoed ideas long associated with establishment conservatives. They can be seen, for example, in his personnel appointments, where he has shown a basically elitist preference for trusted old faculty associates from the University of Chicago and bright young Foreign Service careerists, and in his quiet, but persistent, attempt to promote greater interest in human rights issues.

But, everyone who has worked closely with him seems to agree, the controlling factor in Shultz's thinking is his background as an economist. As one put it, "If you had to sum George up in a phrase, you'd have to say that he's a free trader. He believes that America's security and prosperity depend ultimately on the rest of the world being stable, prosperous and secure.

"He sees different countries, trying to come to terms with failing economies, being pulled toward protectionism, and he believes that can only make the situation worse, that economic hostility among nations now will be echoed later by increasing belligerence on everything from local border disputes to the international arms race.

"It seems to him that there's no more important road to peace than getting everyone--the industrial nations, the Third World, eventually even the communist bloc--to expand trade and growth and employment for their mutual benefit."

The big question is whether Shultz, using his interest in economic problems as a springboard, can absorb other issues in a way that enlarges his world view and enables him to guide the administration toward a concerted foreign policy that will avoid ideological rigidity while remaining true to Reagan's basic conservative vision.

"If you look at the record of what he did on the Middle East initiative and the pipeline dispute, I think you would have to conclude that he's made a good start," asserted the State Department official, who discussed Shultz's relationship with Reagan.

"In both cases, he brought to the problem the qualities of intellect, personality and common good sense that created the climate where you could get an agreement and win support for it.

"Foreign leaders trust him because they know he can see things from their perspective. Liberals, while recognizing he's not one of them, see him as someone with whom they can find a lot of common ground and, most important, the White House knows he's a man who never forgets that it's not George Shultz's policy but Ronald Reagan's policy."

As to the kind of mark Shultz is likely to leave, the official noted, "That depends on a lot of things including how long Reagan remains president. Is Shultz going to be secretary for two years or six years?

"If it's only two years, I think he will leave his successor with some very promising begnnings and, if it's six years, he well could be remembered as one of the greatest secretaries of state."