Clark Clifford, the U.S. presidential envoy, returns to Washington Tuesday believing he has found a formula for bringing a sullen Turkey back into a full-fledged NATO partnership.

Clifford has high hopes that Greek and Turkish Cypriots will begin genuine bargaining at the end of March for a settlement over divided Cyprus. He would regard this as the first breakthrough since the Turkish invasion in the summer of 1974.

If Clifford's expectations are realized, the way could be opened to lift the congressional embargo on arms for the Turks. That, in turn, would enable Ankara to let U.S. forces return to the 26 Turkish bases from which they were ousted after the embargo was imposed.

Clifford stopped off here for talks with the British after a two-week swing through Vienna, Athens, Ankara and Nicosia. His stated objective was to cool the tensions between Greeks and Turks, NATO's southern flank, by getting authentic talks started over Cyprus.

His immediate goal, however, appears to have been clearing the way for a U.S. return to the sophisticated monitoring stations on turkey's border with the Soviet Union.

Clifford, who was told by President Carter to "get right at it," began in Vienna with a suspicious Kurt Waldheim, the U.N. Secretary general. Waldheim is said to have feared that the United States was elbowing the U.N. aside after the international organization had spent 30 months conducting fruitless talks between Greek and Turkish Cypriots.

Clifford is understood to have told Waldheim that the United States intends to keep the United Nations out in front, that Washington wants to maintain a low profile. The crucial round of talks is to begin March 31 in Vienna under U.N. auspices, and Waldheim is now thought to have been mollified.

If Clifford's hopes are realized, Rauf Denktash, the Turksih Cypriot leader and Archibishop Makarios, head of the Greek Cypriots, will for the first time exchange concrete proposals in writing. In the 2 years of talks so far, Clifford found, no written proposals were ever exchanged.

Denktash is seen as an instrument of Turkey in general and the Turkish army in particular. To make Denktash move, Clifford had to persuade the Turks that a Cyprus settlement is in their interests.

The Turks have publicly insisted that there can be no link between Cyprus there can be no link between Cyprus and the supply of U.S. arms. But the congressional embargo specifically states that the ban will not be lifted until some progress is made toward settling the island's fate. Thus, Clifford could only persuade Ankara to spur Denktash by pointing to the congressional condition. In any event, he left Ankara believing that the Turks now think a Cyprus deal is in their interest.

Clifford faced an equally stubborn problem in Makarios who, in effect, has been relying on Congress to pressure the Turks. Clifford is known to have warned the archibishop that "his friends would lose interest in Cyprus," that the island by itself is of "mimimal concern" to Washington.

In effect, Makarios was warned that the predominant U.S. military interest in Turkey must outweigh its concern for Cyprus and that the arms ban against Ankara could not last forever.

Thus, Mokarios is now believed to be convinced that it is also in his interest to produce a specific proposal at Vienna and launch real negotiations.

Both sides acknowledge that Turkish troops occupy almost 40 per cent of the island and have driven out virtually all Greek residents. Both acknowledge that some federal structure must now be erected over self-governing Greek and Turkish zones. Makarios wants to maximize and Denktashto minimize the powers of this central government. The second major issue is how much or how little of their sector the Turks will give back to the Greeks.

Clifford entertains no illusions over the speed with which the Vienna talks will end in an occord. He recognizes that the two sides regard each other with deep hostility.

He has indicated that the United States will maintain its "interest" in bringing the two communities to a deal, both directly and through their patrons in Ankara and Athens. Clifford hopes that the initial round of Vienna talks will run for seven or eight days. If they do, the Carter administration will be better placed to tell Congress that progress is being made, that the arms embargo against Turkey should be lifted.

The Greek-Turkish relationship is complicated by much more than the Cyprus quarrel. In Athens, Clifford was impressed by the emotional fervor of Premier Constantine Karamanlis who seemed to be genuinely fearful of Turkish expansion in the eastern Mediterranean.

Karamanlis icted the amphibious force he said Turkey has created and insisted that it had no relationship to NATO needs, but was poised against the Greek Dodecanse Islands.

The Greek premier also complained of the Turkish seismic ship that took soundings last summer in international waters above what Greece claims is its continental shelf. The premier reportedly said that action will be taken if the ship moves in again, and Clifford regarded that as hoving an omnious sound.

In Ankara, Clifford heard what he regarded as plausible Turkish explanations for these moves and listened to Premier Suleiman Demirel's complaint that the Greeks had allegedly breached a treaty by fortifying their eastern islands.

Clifford made no substantive proposals to solve these knotty problems, worsenend by the felief that there may be oil in the contested waters. However, he is known to have suggested several procedural devices, from arbitration to bringing a case to the World Court, as means for settling the disputes.

In both rival capitals, Clifford warned that "somebody's going to get shot" unless the disputes were settled. An open clash between the tow, Clifford told them, would thoroughly olienate American opinion and could drive the United States from the area.