PRESIDENT REAGAN has a rare and important opportunity to move forcefully against fraud and mismanagement in government. He must appoint a successor to the respected Comptroller General Elmer B. Staats, who is ending a 15-year term as head of the General Accounting Office, the federal government's chief financial watchdog.

This is the longest term appointment in government, and with good reason: the idea is to keep the comptroller general as politically independent and professional as possible. Mr. Staats, whose term expires March 7, upheld this tradition with distinction.

Under a new law, Mr. Reagan's appointment of a successor is subject to Senate confirmation and is to come from a list of at least three names provided by a bipartisan House-Senate commission. Ideally, the nominee should be a politically neutral professional, familiar with the executive and legislative branches and able to administer the "public auditor" responsibilities with which Gao is charged.

The commitment to running a tight and proper operation throughout the federal bureaucracy, shared by Mr. Staats and the new administration, can and should be maintained by the swift appointment of someone who can step in and take over without any unnecessary break in GAO's top leadership.