Anytime there is a new leader in either Moscow or Washington, both capitals can call it a chance for ''a new beginning.'' This time, for good reasons in each capital, both Moscow and Washington grasped the chance provided by the passing of Yuri Andropov to proclaim ''a new beginning'' and to make appropriate gestures of readiness to seek better relations with each other.
In the case of President Reagan in Washington, the good reasons include the virtual collapse of his policies in Lebanon. He can get out with his Marines intact and a modicum of face-saving only with the consent of Moscow.
The way out of Lebanon opened up at midweek as the Lebanese Army collapsed. After consulting the Syrians, the Soviets informed the UN Security Council that they were withdrawing their objections to a UN force taking over the peacekeeping role in Lebanon.
They attached conditions. The existing multinational force of US, French, and Italian troops must leave. (The British had already gone.) And US naval forces would have to leave Lebanese waters.
Washington immediately pronounced the conditions ''unacceptable.'' But the way out was open. After the usual maneuverings, it now seems possible that a UN force will be taking over from the present pro-Gemayel international force.
Moscow too has reasons for seeking ''better relations'' with the United States. To appear to seek such relations can reassure its neighbors, third-world countries, and even its own allies. Any new regime in Moscow needs time to settle in and consolidate. Foreign adventure and anxious neighbors are undesirable.
Moscow's economy is in stagnation and can ill afford the strain of another round in the arms race.
Also, none of Moscow's current foreign ventures seems to be prospering. The Afghan war goes on and drains Soviet resources. Ethiopia is reported to be sending away the Cuban troops Moscow had supplied. Cuba and Vietnam are expensive drains on Soviet resources.
Any new regime in Moscow would logically want a breather. Moscow's new head man, Konstantin Chernenko, behaved logically this week. He exchanged courtesies with US Vice-President George Bush. Both Chernenko and President Reagan played it cool, of course. Mr. Reagan wants ''an agenda'' of substantive issues before he will be ready to meet Mr. Chernenko. Chernenko will be ready only ''for honest talks on the basis of equality and equal security.'' But the emphasis was on readiness to talk.
President Reagan's newly discovered interest in improved relations with Moscow has been stimulated by reversals of his policies in the Middle East, and by a rising danger of both Soviet and US involvement in the Iran-Iraq war.
The worst for Mr. Reagan has been the disintegration of the Gemayel regime. It was the end not only of Reagan's commitment to Gemayel but also of a chapter in Middle East diplomacy which opened when former President Sadat of Egypt made peace with Israel.
Until then, the US had been pursuing peace in the Middle East through a conference in Geneva at which the Soviets were co-chairmen with the US. Moscow was accepted as an inevitable party to negotiations about the area. The Sadat trip to Jerusalem opened the way for excluding Moscow from the area. Camp David represented a solo US effort to broker peace between Israel and its Arab neighbors with no Soviets involved.
Today, with the near-collapse of the Gemayel regime, Moscow is back in the picture. It has supported Syria, which in turn has backed the winning factions in the civil war in Lebanon. The Soviets could exert influence over Syria and, through Syria, on the winning Druze and Shiite militia units.
It was time for Washington and Moscow to talk about ways of controlling events in the Middle East.
Not far away is a companion danger. Iran has launched a major military offensive against Iraq. If it succeeds, what else might the Ayatollah Khomeini think of doing in the sensitive Arab Peninsula? Both Moscow and Washington would be better served by an end to that war than by a military victory for either Iran or Iraq over the other.
The more talk, the less the risk that US and Soviet soldiers might someday find themselves facing each other. It could have happened in Lebanon. The Marines there are within shooting range of Soviet soldiers in Syria. Quiet conversations might reduce the times and places where this kind of risky proximity can occur.