ISRAELI'S FRAGMENTED electorate has turned out the stale and discredited Labor Party, in power since the state was established in 1948. The voters gave a thin plurality to the generally right-wing bloc known as the Likud. Its chief, former underground leader Menahem Begin, 64, must decide whether to seek a unity government with Labor, or a coalition - or something . Mr. Begin is an ideologue - some would say a primitive - who has had the luxury of indulging old dreams and the easy slogans of opposition. He has never had to govern. Whether he can be educated in the complexities of the issues, and even whether he can harness the disparate factions within the Likud, is unclear.

Though the elections were fought mainly on domestic issues, international attention has correctly focused on Likud's record of refusal to contemplate even the modest territorial concessions considered by Labor. It's a question of degree: Neither party supports other than "defensible" borders and neither supports a Palestinian state, but Labor has been more sensitive, and sensible, about keeping the Washington link strong. There are two ways of looking at this. One is that Likud's elevation is a disaster, sure to strengthen Arab extremists, undermine Arab moderates and intensify American-Israeli strains. The other is that negotiations can proceed more surely with a Likud whose flank is secure than with a Labor government exposed to Likud attack - it took a Nixon to go to Peking. We don't find this second view particularly persussive at the moment. But we note it. The circumstances are novel and volatile.

For the United States the path is reasonably clear. The administration, wisely, had let Israelis know before their elections what its broad policy would be. The Israelis could have been under no illusions when they voted that President Carter would not continue down that track. American policy cannot ignore political realities in one or another Mideast country but even less can it ignore the international realities that demand deliberate pursuit of a settlement. Arabs, some more and some less, have committed themselves to cooperate with American diplomacy. To hesitate on account of Israel's political turn would be to renege on a pledge on which various Arab leaders have bet heavily. The special American commitment to Israel's security remains intact. But the Israelis, as they start to bargain out a government, must understand that the United States' search for a settlement goes on.