Griffin B. Bell won confirmation as Attorney General from a divided Senate yesterday, only to find himself facing a sensitive new problem - a possible clash with FBI Director Clarence M. Kelley over Kelley's departure from the FBI.

The potential confrontation was precipitated by Kelley, who sent Bell a letter stating that he does not intend to retire as FBI director until Jan. 1, 1978. That ran directly counter to the widespread impression that Bell and President Carter want to put their own man at the head of the embattled FBI at a much earlier date.

The problem with Kelley surfaced as the Senate confirmed Bell by a vote of 75 to 21. The approval came only after a heated debate in which some senators blasted Bell's civil rights record, challenged his judicial ethics and raked over his appointment as an act of political cronyism by Carter.

With the confirmation of Bell and the swearing in yesterday of Joseph A. Califano Jr. as Secretary of Health, Education and Welfare, 10 of Carter's 11 Cabinet nominees have been approved. The last, F. Ray Marshall of Texas, is expected to be confirmed as Secretary of Labor by the Senate today.

Bell, a 58-year-old Atlanta lawyer and former federal appeals court judge, was the most controversial of the Cabinet choices - a fact underscored by the substantial number of votes against him yesterday.

His nomination was vigorously opposed by several civil rights groups, and their charges were echoed by the two Republican senators. Charles McC. Mathias Jr. (Md.) and Edward W. Brooke (Mass.), who led the assault on Bell in yesterday's debate.

They said they opposed Bell because he had been an adviser to former Georgia Gov. Ernest Vandiver during that state's "massive resistance" to school desegregation in the late 1950s; because his decisions as an appeals court judge from 1962 to 1976 had an allegedly anti-civil rights cast, and because he had upheld the attempt to bar Julian Bond, a black, from the Georgia legislature for anti-war statements.

They also criticized him for failing to disclose for six years that he had received free memberships in two Atlanta clubs that exclude blacks and other minorities, for failing to disqualify himself from a 1976 case involving a similar club, and for failing to excuse himself from ruling on a 1963 Georgia desegregation case, although he had advised state officials on the issues in that case before becoming a judge.

While these charges were ebing rehashed on the Senate floor, Bell's position as the Carter administration's biggest magnet for controversy received a boost from another quarter - revelation of the letter from Kelley.

Authoritative sources said last night that Kelley, in setting next Jan. 1 as the time for his retirement, has acted on his own initiative without consulting Bell. Kelley's aim, the sources said, was to tell Bell of his intentions; and, some sources added, put the new Attorney General on notice that he will resist efforts to remove him from the FBI directorship before that time.

Testifying before the Senate Judiciary Committee two weeks ago, Bell said that Kelly would give way to a new director "before too long." Although he deliberately avoided specifying a timetable, Bell's remark was widely interpreted as meaning that the changeover would take place in the near future.

Now, Kelley's letter confronts Bell with some sensitive choices. If he allows Kelley to remain until the end of the year, his action is likely to be interpreted as a backing down in the face of a challenge from the FBI director.

In addition, there is widespread feeling in law enforcement circles that Kelley's now-stated intention to retire at the end of the year would put the crisis-ridden FBI in the position of being run by a lame-duck director without influence or authority.

On the other hand, should Bell attempt to force Kelley out against his will, he would risk charges that the Carter administration is trying to bring the FBI back under the sway of partisan political influence. Such charges were heard in yesterday's Senate debate, and Kelley is understood to have made his move partly because he feels that he can count on congressional support.

Bell's reaction was to temporize by having his aides issue a statement yesterday noting that Bell does not have the legal authority to dismiss Kelley and stating that Bell "will set in motion a procedure for the orderly transfer of the directorship of the bureau." But the statement said nothing about when the new administration wants Kelley to leave.

Kelley, 65, became FBI director in July, 1973, and is serving under a law that grants the director a single term of 10 years. It was unlikely that he would have served the full term in any case, since the law states that an incumbent must retire at age 70 unless the President waives that requirement.

However, Senate sources familiar with the history of the law say categorically that the 10-year term does not preclude a President from firing the director. The FBI, they note, is part of the executive branch and its director serves at the pleasure of the President.

However, the sources note, by specifying a 10-year term the Senate did intend to insulate the office somewhat from political considerations.

Another complicating factor involves Kelley's pension. Under a new federal law, the three years that Kelley has served as director would allow his pension from earlier FBI service to be recomputed on the basis of the higher director's salary.

But the law does not take effect until Oct. 1, and Kelley would have to remain in active federal service until that date to take advantage of its provisions.

For that reason, Bell is believed to be planning to keep Kelley at the FBI in some sort of emeritus or advisory slot that would open the way for appointment of a new director.

In the Senate debate, some Republicans taunted Democratic liberals, most of whom voted for Bell although obviously uncomfortable with the appointment, for applying "a double standard."

Brooke and Sen. Bob Dole (R-Kan.) both noted that when Southern Supreme Court nominees with backgrounds similar to Bell's were sent to the Senate by a Republican President, Richard M. Nixon the Democratic majority rejected them.

Said Brooke, "I think that a Republican nominee who had engendered this kind of controversy and contradictory testimony may have been summarily rejected by this Congress."

Dole added, "Would this Senate have confirmed if President Ford had won and nominated a man with the same background . . . who belonged to restrictive country clubs . . . a close political associate, a man who contributed a substantial amount to the President's campaign? I think the answers are obvious."

"The American people are tired of watching brothers, campaign managers, law partners and old friends sprinting the inside track to the Justice Department," said Lowell P. Weicker Jr. (R-Conn.).

Mathias, in summing up the opposition, asked, "Do we automatically have to give our consent" to a Cabinet appointee merely if he "is not a convicted felon . . . or lunatic?"

On the other side, Birch Bayh (D-Ind.), who led a successful fight against two Nixon Supreme Court nominees from the South several years ago, argued that the evidence showed Bell had tired to act as a moderating influence on Vandiver during the "massive resistance" period.

"Perhaps we should not be so pious as to the standards of people 25 years ago who lived in a different part of the country," declared Bayh.

Before approving Bell, the Senate killed, 71 to 24, a move by Brooke to recommit the nomination to the Judiciary Committee.