Centre Glenn Mulvenna was the prototypical good all-round hockey player, who possessed better than average skating skills, a commitment to defense and would on occasion chip in with the odd goal or two. He carried a strong on-ice work ethic while playing his minor hockey in Calgary and made the jump to major junior in 1984-85, joining the New Westminster Bruins of the WHL. As a 17-year-old rookie Mulvenna suited up for 66 games, tallying 16 goals and 31 points. Near the end of his third year with the Bruins, he was traded to the Kamloops Chiefs for the final 18 games of the year.
Despite putting up decent offensive statistics, Mulvenna was unable to convince an NHL club to draft him during his time in Junior A. He decided to return to Kamloops in 1987-88 as the team's overage player and contributed 59 points in 38 games. In 1988-89 Mulvenna turned pro, suiting up for both the Flint Spirits and Muskegon Lumberjacks of the IHL. His first shot at the NHL came during the 1991-92 season when he was called up for one game by the Pittsburgh Penguins.
Mulvenna realized he had virtually no hope of cracking the strong Penguins' lineup on a regular basis. The team had won two consecutive Stanley Cups and were not looking to tinker with success so he signed a free-agent contract with the Philadelphia Flyers in the summer of 1992. Again, Mulvenna was unable to earn a roster spot but was inserted in to one Flyers game during the year.
Although Mulvenna never again made it to the NHL, he continued to play professional hockey through the 1999-00 season, playing the final three years of his career in the British League. After retiring, he took over as an assistant coach with the Newcastle Jesters, learning the ropes of the job behind the bench. The Jesters disbanded after the 2000-01 season, but the apprenticeship paid off as Mulvenna was offered the head coaching job with the Peterborough Pirates in 2001-02.