He had an outstanding junior career with the Toronto Marlboros of the Ontario Hockey Association, eventually captaining the team to the 1967 Memorial Cup.

As a pro Glennie went on to play 572 career NHL games, all but 18 with the Toronto Maple Leafs, scoring 14 goals and 100 assists for 114 points.

Glennie, a defensive, hard-hitting defenceman was often paired with the offensively-skilled defencemen on the Leafs, such as Tim Horton, Börje Salming and more frequently former Marlboro teammate Jim McKenny.

[1] Glennie sustained a mild concussion in the second period of a 7–3 win over the Detroit Red Wings at Maple Leaf Gardens on November 5, 1975, after Dan Maloney attacked him from behind, flattened him with a right-hand punch, hit him several more times and repeatedly lifted and dropped him to the ice.

Maloney, who claimed the force of the contact was excessive and that he had no intention of injuring Glennie, was charged with assault by Attorney General of Ontario Roy McMurtry the following day on November 6.