DALLAS (AP) _ Financially ailing First RepublicBank Corp. said Tuesday it expected to post a $1.5 billion loss in the first quarter, and that its chairman resigned as part of a management shakeup arranged by federal regulators.

The projected quarterly loss, which would be the sixth-largest ever by a U.S. corporation, was nearly three times higher than what First RepublicBank officials had predicted earlier.

The bank holding company, the nation's 14th largest in terms of assets, attributed the loss to a 50 percent increase in its loan-loss provision, to $231 million, and writedowns from foreclosed properties, all totaling $1.5 billion.

''It's a very big loss, and obviously it will require a recapitalization of the bank,'' said Comptroller of the Currency Robert L. Clarke, whose office last week completed a two-month examination of First RepublicBank.

After that scrutiny, ''it was obvious to me and to my colleagues at the FDIC and the Federal Reserve Board that management needed to consider carefully the steps that would have to be taken to get on with the business of restructuring. Certainly one of the steps that had to be considered was a change in the leadership of the company.''

First RepublicBank said Albert V. Casey, 68, former chairman of AMR Corp., which operates American Airlines, was elected by the board to replace Gerald W. Fronterhouse, who resigned as bank chief executive and chairman as part of a management shakeup arranged by federal regulators overseeing recapitalization of the company.

''I made the decision to step aside at this time because it is in the best interests of this institution and the community that I do so,'' Fronterhouse said.

Casey said Fronterhouse made a ''great personal sacrifice'' by resigning. Casey said his goal is ''to return to profitability and to provide the state of Texas with a stronger and much-needed banking institution.''

On March 17, the Federal Deposit Insurance Corp. made a $1 billion six- month loan to First RepublicBank to quiet depositors' fears and halt a run on deposits. Reeling from the effects of nearly $4 billion in non-performing loans in oil and real estate markets, the bank reported a loss of $656 million in 1987.

FDIC Chairman L. William Seidman last month estimated the First RepublicBank bailout will cost a total $1.7 billion. The FDIC's assurance of full protection of all depositors and other general creditors of the company's affiliate banks has enabled the banks to continue service without disruption, officials said.

But part of FDIC's deal with First RepublicBank officials specified that its most senior executives would resign if asked to by the FDIC.

Casey also announced the board's appointment of a new executive committee with Casey the chairman and Mark Shepherd Jr., chairman of Texas Instruments Inc., the vice chairman.

Others on the new board include: James R. Adams, president of the Texas division of Southwestern Bell Telephone; James F. Chambers, chairman of the executive committee of the Dallas Times Herald; Robert Crandall, chairman, president and chief executive officer of American Airlines; W.C. McCord, chairman and president of Enserch Corp.; and Paul R. Seegers, chairman and chief executive officer of Centex Corp.

Fronterhouse, 51, was a 26-year veteran of the banking firm, having spent his entire career there. He succeeded James D. Berry as chairman of predessor RepublicBank Corp. in July 1986.

He was the latest in a series of top management officials to leave. Three weeks ago, Charles H. Pistor Jr., 57, chairman of flagship bank First RepublicBank Dallas, announced he would leave in mid-April. Fronterhouse was to have assumed his duties.

With Fronterhouse and Pistor gone, only vice chairman Joseph R. Musolino would remain of the trio who rose to the center of the bank's top management in the early 1980s.

Fronterhouse had beat out Pistor and Musolino for the chairmanship of RepublicBank in 1986.

Fronterhouse led RepublicBank when it acquired cross-town rival InterFirst Corp. in December 1986. The deal was designed to create an earnings machine through accounting, adjustments and cost-cutting, including the elimination of duplicate jobs - about 3,000 jobs, in all.