PERHAPS the Civil Rights Commission has completed its work. It's possible to argue that the commission's contributions over 24 years have brought its job to an end--and, if it has not resolved the great central questions of equality in American society, they have been transformed and passed on to other hands.

Last week President Reagan fired the commission's chairman--Arthur Flemming, a man of long and devoted service to the country--with a press release, and named a successor, Clarence M. Pendleton, the president of the San Diego Urban League. Although the action itself, as it affected Mr. Flemming, was graceless and raw, this is still not a bad moment for people who have admired the commission and its work to ask where it seems to be going. Mr. Flemming's own appointment in 1972, displacing the Rev. Theodore Hesburgh, incited fears that the commission was being silenced. Those fears proved unfounded, and similar fears this time may well turn out the same way. The changes in the commission have been less important than the changes in the world around it.

When this country emerged from World War II, Americans had not yet decided whether there was a national responsibility to do anything about racial segregation imposed by law. Americans had not even decided whether the federal government had jurisdiction in the key areas--racial discrimination in voting, in education, in access to public accommodations and all the rest.

"We are none of us entirely familiar with just how far the federal government under the Constitution has a right to go in these civil right matters," President Truman said in 1947 when he set up his Committee on Civil Rights. Ten years later, in the first civil rights bill passed since Reconstruction, Congress re-created the Truman committee in the form of the commission that Mr. Reagan is now treating rather casually.

To assess the commission's work in the early years, you have to keep it in mind that few Americans knew much about the ways in which the actual mechanisms of legal discrimination operated, or the deforming effects they had on people and communities. Data on voting practices, now on the shelves of every public library, were either not available or were only in the process of being collected-- often at some personal risk to the people doing it. Simply by gathering information, the commission contributed powerfully to the passage of the 1964 Civil Rights Act and the 1965 Voting Rights Act.

With them, the nature of the challenge began to change. The dismantling of unconstitutional law proceeded rapidly. But dealing with the next range of questions--the questions of social and economic inequality--was harder to address within a strictly legal structure. You may remember the report several years ago complaining about television comedies and their lamentable failure to portray women, minorities and everybody else as they would be in an ideal world. The great work of defending the citizen's constitutional rights had meanwhile been fully engaged by the courts, by Congress and state legislatures, and by agencies at every level of government.

Is there still a role for the Civil Rights Commission? What is it? How can the commission be revitalized? Should it be? As it takes up Mr. Pendleton's nomination, Congress could do worse than to address these questions.