Before attending college, Royal enlisted in the Air Force after graduating from high school in 1943. In the Air Force, he attained the rank of staff sergeant. Royal graduated from Oklahoma in 1950 where he lettered on four conference championship squads from 1946-49. Royal was an all-conference quarterback in 1949 when the Sooners finished 11-0. After graduation, Royal served one-year stints as an assistant at North Carolina State, Tulsa, and Mississippi State. In 1953 Royal moved to the Canadian pro league as head coach at Edmonton where he went 16-5 and won the Western Division Championship. In 1954 he returned to Mississippi State as head coach and went 12-8 over two seasons. In his one season at Washington the Huskies went 5-5-0. Royal then decided to settle down at Texas where he was head coach from 1957-76 and compiled a 167-47-5 record that included 11 Top 10 finishes, three national championships, 11 Southwest Conference crowns and 16 bowl games. He also served as Texas Athletic Director from 1962-80. In 1980 he was named a special assistant on athletics to UT President Peter Flawn. Royal was inducted into the College Football Hall of Fame in 1983.