In the wake of Iraq's crushing defeat in the Persian Gulf war, there is a growing feeling in the region that the old order of things has been shaken up and - for the moment at least - there is an exciting mixture of new possibilities, a chance for real peace.

At the very top of the list is a renewed sense of hope that the Israeli-Palestinian issue might, at long last, be open to settlement. Secretary of State James A. Baker III leaves this week to visit the region. The Palestinian question will be a major topic.War left the United States as the unmatched military power in the Middle East, having easily ruined Iraq's mighty military machine. The rapid, awesome conquest left the Soviet Union, anti-American Arabs, and even Israel, sitting on the sidelines to some degree.

As one official put it: "We have a new credibility in the Middle East because we have demonstrated that we are an ally to count on."

How the credibility is spent is the real issue. Arab states want the United States to push Israel into resolving the Palestinian question. The Bush administration says it does not want to "impose" a settlement, but it clearly has the power to do some arm-twisting with Israel.

The United States can point to the fact that it has Israel's security in mind, citing the rushing of Patriot missiles to the country to deal with Scud attacks, the heavy economic and military aid and the destruction of Iraq's army, the major threat to Israel in the region.

This certainly ought to give the United States the right to ask Israel to recognize the necessity of the Palestinian people to their own homeland and to comply with United Nations resolutions to that effect.

But it is not that simple.

The voice of the Palestinians, the PLO, is a terrorist organization whose charter calls for the destruction of Israel. The PLO sided with Saddam and cheered on the Scud missiles falling on Tel Aviv. Several wars have been fought with Arab neighbors to eradicate Israel from the face of the Earth. Giving up the West Bank and other occupied places could make Israel vulnerable.

Yet things change. Egypt long ago made peace with Israel. Iraq has been reduced to shambles. A Palestinian homeland would eliminate any excuses for further adventures by an already-discredited Saddam.

Even Syria and the strategic Golan Heights issue is less of a problem than it used to be. The Soviet Union no longer can afford to heavily support Syria, which is now turning more to the West. In any case, the Soviets have begun to restore diplomatic relations with Israel. The Kremlin appears to be turning away from simply using the Middle East as a place to foment trouble.

Within Israel, a fierce debate is raging over what direction to take. There are the usual hard-liners who want to continue the "no retreat" policy that simply refuses to deal. That group is powerful since it is headed by Prime Minister Yitzhak Shamir, who has rejected U.S. proposals for Israeli-Palestinian talks.

This group says that while American help has been profound, the United States also owes Israel for staying out of the gulf war even though it was attacked by Scud missiles, thus helping Washington keep the Arab allies in the coalition against Iraq.

Others in Israel argue that it is time to respond in a positive way to the new situation. After all, they say, the Palestinian question is not going to simply disappear and there must be an end to the fighting someday. That approach makes good sense.

Peace can only come when Israeli hard-liners and PLO fanatics quit trying to kill each other and look instead for answers that will put to rest the deepest fears of both sides. That should not be an impossibility - as the Israel-Egypt experience shows. The United States should seize the present opportunity for change and push hard.