Civil Aeronautics Board member Lee R. West has submitted his resignation to President Carter, sources said yesterday.

West's departure will give Carter an opportunity presidents seldom get to remake an independent regulatory agency through the appointments process in a very short time. The vacancy will give Carter the opportunity for a fourth appointment to the five-member agency since taking office last year.

Carter has yet to name a replacement for G. Joseph Minetti, who reached the mandatory retirement age of 70 almost a year ago but whose tenure on the board has been extended several times by presidential waivers. His current waiver expires May 1. Minetti has been on the board since 1956.

West, a Democrat like Minetti, was an Oklahoma state judge when he was appointed to the board by Richard Nixon in 1973. His letter of resignation, effective at the end of June, was described as laudatory of the administration's and the CAB's current policies favoring competition and low fares.

Since taking office, Carter has appointed the CAB's current and highly regarded chairman, Alfred E. Kahn, and Elizabeth E. Bailey, the first woman member of the agency since it was created in 1938.

The fifth member of the agency is Richard J. O'Melia, a Republican who had served as a member of the CAB staff for 16 years before being bamed to the board in 1973.

The CAB under Kahn's leadership has moved to increase competition in the highly regulated airline industry. Along with the administration, however, the CAB has told Congress that new legislation to prevent a less competition-oriented board from undoing the current work.