He served as a chairperson of the Wyoming Republican Party from 1967 to 1971. After stepping down as chairperson, Brimmer was nominated by the 27th Governor of Wyoming, Stanley K. Hathaway, to serve as the attorney general for Wyoming. He succeeded James E. Barrett and served until 1974, when he was succeeded by David B. Kennedy. He then was nominated by Gerald Ford to serve as the United States Attorney for the United States District Court for the District of Wyoming until 1975.
