The leadership of Israel's centrist Democratic Movement for Change voted today to join the coalition government of conservative Prime Minister Menahem Begin, a move that will give him a comfortable parlimentary majority and lessen his dependency on conservative religious parties.

It could also offer a new option in the clouded question of possible succesion to Begin, 64, who has just returnel to work after hospitalization who whose health remains uncertain.

Begin met today with the leader of the Democratic Movement, Yigael Yadin to dicuss the party's entry into government. The party's secretariat and 15 members of Parliament voted today to join Begin's coalition and its general council is to act on the issue Thursday.

Although similar efforts have failed twice in the past, the betting here tonight is that the Democratic Movement will join despite violent opposition of some members.

Yadin apparently is willing now to accept the same terms he refused several weeks ago. he said "grave pulitical issues" at home and abroad argue in favor of political unity.

Yadin is looked on as a relative dove on on Middle East issues but he has said that his party has few basic differences with Begin's government on foreign policy.

Begin has shown that he can rule without Yadin's party, strengthening his position for the current bargaining. He had kept three ministries open for the Democratic Movement since coming to power in elections last May, but announced recently that those posts would be filled Monday regardless of what the Democratic Movement decided.

The succession issue, however, is another new factor in the maneuvering of the parties.

The morning papers show photographs of Begin back on the job after 20 days of hospitalization and convalescene, but his latest illness has raised a serious questions: What would happen shoul he die or be forced to step down because of oill health?

Begin had a serious heart attack just before the May elections and he has been hospitalized twice since then for inflamation of the membrance surrounding the heart.

There is no depth of leadership in the Begin government to compare to the rival Labor Party, which ruled from the birth of the republic in 1948 until last May.

As one observer commented, the Likud Party leaders of the ruling coalition "stayed in opposition too long and came to power too late." Of the young, dynamic founders of Begin's anti-British underground of the 1940s, only Begin remains active.

The Likud itself is a coalition of parties and the second man in Begin's dominant Herut faction is Ezer Weizman, the minister of defense. The head of the Likud's Liberal faction, Finance Minister Simcha Ehrlich, stood in for Begin at Cabinet meetings during the last illness.

Neither has the national stature that would make them automatic successors, however.

The best know national figure in the government is foreign Minister Moshe Dayan, but he has no political base, having left the Labor Party to join the government, and his succession to the premiership would be bitterly opposed by the Likud Party itself.

Some political observers say that if Begin dies, the Likud would fall apart and new elections would quickly follow. Others say Begain would stay on as prime minister even if he were incapacitated rather than have his party face the succession issue.

There is now another possibility, Yadin at one point was promised the deputy premiership. If his party does join the government, this could mean that Yadin would fill in should Begin fall ill again. If Begin were forced to step down, Yadin might even become prime minister with the help of Likud's Liberal faction.

This is no certainty, however, and therefore there is no real answer to the question of what would happen should Begin leave the political scene.

In the meantime, the Democratic Movement leaders think that they could give the government a moderate tone as well as lend it some needed administrative talent.

Three months after the election, the Likud government has not put together a team to come to grips with domestic and economic issues.