Early last month, Hamilton Jordan flew to Riyadh, Saudi Arabia, to join President Carter in the midst of the president's extensive foreign trip.

It was not a happy time for Jordan, Carter's 33-year-old chief political adviser. His flamboyant personal behavior had become a regular topic in the newspapers. His marriage was coming apart. There were suggestions by some that he might be in over his head at the White House.

That night in Riyadh, Jordan tagged along with the presidential party to a state dinner given by top Saudi officials. It was one of those rare occasions when Jordan decided to wear a tie, but he could not bring himself to bow completely to custom. The tie was loose and his collar open, as if he was off to the neighborhood bar for a few beers after work. There was not, according to someone who was there, even a glimmer of disapproval from the president.

Jimmy Carter has never publicly shown any displeasure with Jordan, or anyone who works for him, for that matter. And now, just a few weeks after what appeared to be the low point in his career as a presidential assistant, Jordan's power inside the White House has been enhanced, the direct result of a presidential order.

By Carter's orders, Jordan is now a regular participant in the weekly foreign policy meeting the president holds with Vice President Mondale, Secretary of State Cyrus R. Vance and national security adviser Zbigniew Brzezinski. Jordan calls this "just formalizing my role in foreign policy," but it clearly will involve him more deeply and earlier in the process of shaping the administration's foreign policy ventures.

Also by presidential fiat, Jordan has taken over running the Monday morning meetings of Carter's senior staff, giving the meetings, despite his easygoing, wisecracking personal style, a much more serious tone. "They have gone from being like group encounters to working sessions," one official said.

In and of themselves, these may seem to be no more than minor adjustments, which is the way Jordan characterizes them. But they mask a new aggressiveness by Jordan and his political staff aides, who are being consulted now on an increasingly broad range of issues. They also spring from a recognition in the White House that the loose staff structure of the first year of the Carter presidency did not always function smoothly and that the president suffered as a result.

Carter came to Washington committed not to have a "chief of staff," which conjured up images of Richard M. Nixon and H. R. Haldeman. Carter said his senior aides would be equals, each reporting directly to him.

What the new president and those around him may have failed to realize then is that to a remarkable extent the White House is a compartmentalized place, with each aide all but overwhelmed with his or her responsibilities. If the system is designed so that only the president is supposed to know everything that is going on, some things are bound to slip through the cracks.

Two examples come to mind from Carter's first year. One was last fall's American-Soviet communique on the Middle East, which caused a predictable uproar among American Jews. It came entirely from Brzezinski and the National Security Council staff. Jordan, who is supposed to offer advice on the domestic political implications of foreign policy, was not even consulted.

"The joint communique triggered him to get more involved in the Middle East," one official said of Jordan. "It was a red flag for everyone around here!"

The second example is the White House's inept handling of the so-called "Marston affair" - the ouster of Republican David W. Marston as the U.S. attorney in Philadelphia. It is not known whether Jordan might have handled it differently, but the fact remains, as one presidential assistant put it, "there was no mechanism to get a warning to Hamilton." Now, presumably, there will be.

Carter still will not have a "chief of staff." Jordan refers to the change in his roles as "increased coordination," and domestic policy adviser Stuart Eizenstat, who along with press secretary Jody Powell pushed hard for the expansion of Jordan's authority, calls him the "staff coordinator."

Whatever name they choose to apply to it, Jordan's enhanced role, more than ever, makes him the president's most important aide.

Jordan insists that any enlargement of his duties in the White House will not be at the expense of others. But in any shift like this in any organization there are bound to be some losers, and two of them would appear to be Brzezinski and White House counsel Robert Lipshutz.

Brzezinski has now been told in unmistakable terms that Jordan is to be a part of the White House foreign policy apparatus. Never again is there likely to be another joint communique on the Middle East sprung whole from the NSC. Nor, for that matter, is there likely to be a repetition of what happened last spring, when Carter and Energy Secretary James R. Schlesinger Jr., working in virtual isolation, put together the administration's energy plan.

The mild-mannered and likable Lipshutz is the oldest, by more than a decade, of the president's senior aides and it was he who was supposed to preside, in a vague sense, over the internal staff. Now that pretense has been dropped and Lipshutz clearly relegated to the relatively narrow legal concerns that come to the White House.

Just what Jordan does in his new role as "coordinator" in the White House remains to be seen, but there have been some clues.

One of his first moves was to organize two days of seminars held last week for staff aides at which Mondale, Eizenstat and Brzezinski spoke. Everyone who works in the White House and the Executive Office Building was invited. It was a tacit admission that below the most senior levels morale has not been that good in the Carter White House, where scores of people who work for the president have never laid eyes on him and have only the sketchiest notion of what the administration is doing.

Also apparently at Jordan's instigation, Carter has been seeing a much broader range of people, if only briefly at receptions. Over the past few weeks these have included get-togethers with Polish Americans, officials of the International Ladies Garment Workers Union and a group of Machinist Union officials, among others.

Recently, too. Jordan dispatched one of his deputies, Landon Butler, to Geneva to become better acquainted with the strategic arms limitation negotiations. It was another sign of Jordan's increased role in foreign policy.

"Like everything else in this town, my role has been greatly exaggerated," Jordan said in a recent interview. He has not, on the surface, changed at all. He is still the only regularly tieless presidential assistant, still a wisecracking country boy from Georgia. "I am just a guy who is going to hold a lot of meetings," he says.

But others in the White House see it as more than that and, for the most part, welcome the change. There has never been any question of Jordan's access and clout with the president. But until now he deliberately defined his job in loose terms, bouncing from one issue to the next, often acting as a White House fireman when crises arose.

"There is a perception across the board that the president will not have a chief of staff, but that despite things that could have been expected to have hurt Hamilton, the president is relying on him not less but more and more," one aide said.

"He is taking on more line responsibility. He's the power here because the president trusts and relies on his judgment. Carter wants political factors figured in across the board, and that's what Hamilton does best."