Glover began his hockey career in the Quebec Junior Hockey League, where he played for the Montreal Nationale. He then moved on to play for the Montreal Royals in the Quebec Senior Hockey League. In 1957, he signed with the Montreal Canadiens of the NHL, but he spent most of his time playing for their minor league affiliate, the Rochester Americans.
In 1960, Glover was traded to the Boston Bruins, where he played for two seasons before being traded to the Detroit Red Wings. He played for the Red Wings for four seasons and was named to the NHL Second All-Star Team in 1965. In 1967, he was selected by the Minnesota North Stars in the NHL Expansion Draft.
Glover played for the North Stars for three seasons before being traded to the St. Louis Blues in 1970. He played for the Blues for two seasons before being traded to the New York Rangers. He played for the Rangers for one season before being traded to the Los Angeles Kings.
In 1972, Glover signed with the WHA's Minnesota Fighting Saints. He played for the Fighting Saints for two seasons before being traded to the Calgary Cowboys. He played for the Cowboys for one season before retiring from professional hockey in 1974.
Throughout his career, Glover was known for his physical play and his ability to play both defense and forward positions. He was also known for his leadership skills and was named captain of the North Stars and the Fighting Saints.
After retiring from hockey, Glover worked as a scout for the NHL's Vancouver Canucks and the WHA's Edmonton Oilers. He was also involved in coaching youth hockey in Minnesota.
Glover was inducted into the Manitoba Hockey Hall of Fame in 1985 and the Manitoba Sports Hall of Fame in 1990. He passed away on December 30, 2001, at the age of 65.
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