Redmond played 13 seasons in the NHL, beginning as a first-round pick, 5th overall, in the 1969 NHL Amateur Draft by the Minnesota North Stars. He was traded in 1970 to the now-defunct California Golden Seals, and from there he was traded to the Chicago Black Hawks in 1972. In five seasons with the Black Hawks, Redmond played in 341 games and accumulated 227 points with 218 penalty minutes. After his stint in Chicago, Redmond was traded and ended up with the Boston Bruins, where he finished his career.