During World War I Magee served in the United States Navy as a seaman first class and small arms instructor. After the war he homesteaded in Bighorn Basin, Wyoming, and worked as a laborer for the United States Reclamation Service in Deaver, Wyoming.
He also resumed his education after the war, studying law at the University of Missouri. He was admitted to the bar in 1922, and commenced practice in Unionville, Missouri. Magee owned and operated his family's farm beginning in 1932, and was postmaster of Unionville from 1935 to 1941.
In 1941 Magee was charged with in the fatal shooting of his cousin Charles Magee. He was acquitted on a plea of temporary insanity. Evidence at his trial indicated that Clare shot Charles Magee when Charles was in police custody, and that Charles was distraught because Charles had stabbed Clare's brother, Dr. E. H. Magee. (Dr. Magee recovered.)
Magee joined the Army for World War II and served as a private in the Field Artillery. He was subsequently commissioned as a captain in the Army Air Corps, and served until the end of the war.
In 1948 Magee was elected as a Democrat to the Eighty-first Congress. He was reelected in 1950 to the Eighty-second Congress, and he served from January 3, 1949 to January 3, 1953. Magee was not a candidate for renomination in 1952. During his Congressional career he earned recognition for his efforts to extend G.I. Bill benefits to veterans of the Korean War.
After leaving Congress Magee resumed the practice of law. He died in Unionville on August 7, 1969, and was buried at Unionville Cemetery.