WHAT IS unique about the Cyprus crisis is the extent to which it is bound up with the diplomatic and political style of one man, Henry Kissinger. This is said not to initiate a round of recrimination, which nobody needs, but rather in the spirit of a remark made many years ago by Henry Stimson, when he was asked, "How on earth can we ever bring peace to the world?" He replied: "You begin by bringing to Washington a small handful of able men who believe that the achievement of peace is possible. You work them to the bone until they no longer believe that it is possible. And then you throw them out and bring in a new bunch who believe that it is possible." Leaving aside how applicable it may be to Mr. Kissinger's frame of mind when he left office, Mr. Stimson's prescription may well be relevant to any number of international disputes and conflicts now seemingly deadlocked. For today, it is enough to note that no sooner had a "new bunch" moved in than, suddenly, the prospects for some movement on Cyprus started looking up. A new American initiative has been launched, with the naming of a special emissary, Clark Clifford, to explore the opportunities of settlement. Almost overnight, the Greek Cypriot majority, huddled in the South, and the Turkish Cypriot minority, settled behind the Turkish occupying army in the North, have started recalculating their odds. So have their patrons in Greece and Turkey. The upshot is that a situation that looked virtually incurable and fraught with peril only a month ago has about it a cast of cautious hope today.

The key has always been in Ankara. As long as Turkey saw that the United States was tying the full resumption of U.S.-Turkish military cooperation to renewed American access to Turkish bases, rather than to progress on healing the Turkish-inflicted wound on Cyprus, then things only got worse. Congress, controlled by forces demanding a rollback of the Turkish occupation of Cyprus, defied Mr. Kissinger on arms and aid for Turkey. The Turks responded by closing bases used by United States and by edging toward the NATO exit door. Efforts to promote talks on the island got nowhere.

But Mr. Carter said during the campaign, and Secretary of State Cyrus Vance has just restated, that progress on Cyprus must be made before questions of arms and aid can be addressed. Obviously with this in mind, Turkey on Jan. 27 allowed the leader of the Turkish Cypriot minority, Rauf Denktash, to meet with the Greek Cypriot president, Archbishop Makarios. It was the first such meeting in 13 years, and another is planned on Feb. 12. Various compromise formulas are being discussed to allow two communities to live side by side in peace under the same governmental roof. The Turkish political opposition is no doubt tempted, as usual, to denounce any display of moderation as a sellout. But there are signs, small but promising, that the Turks realize that the wind from Washington has shifted and that this may be in the time to cut the appaling losses in international prestige, in defense readiness and in access to the European economy that their Cyprus policy has inflicted upon them.

The Cyprus crisis is often perceived as the product of profound ethnic rivalries, which are also held accountable for the host of other problems that have rent Greek-Turkish relations and decimated the eastern Mediterannean corner of NATO in recent years. One does not want to dismiss the ethnic factor: Without it there would have been no crisis. But the proximate cause of the crisis was a flawed American policy, and its solution became hopelessly ensnarled in executive-congressional combat. This makes it easier, not harder, to try to fix now. A sensible policy is not only likely to untangle Greeks and Turks but to dissolve the executive-congressional snarl. It is a time for quiet diplomacy and meaningful consultation with Congress. Unlike, let us say, the Arab-Israeli conflict, the Cyprus dispute, for all the bitterness that has compounded it in the past, may not be quite as intractible as it has sometimes been seen - or made - t be.