After playing hockey at the junior level for the
Kenora Thistles, Allison caught the attention of the
Sudbury Wolves, who made him their first
draft pick in the 1978
OHL Draft. Playing on the left wing, Allison had an exceptional second season in Sudbury, achieving 95 points, on the strength of 71 assists, and was drafted by the
New York Rangers in the second round of the
1980 NHL entry draft. Allison began his
National Hockey League career the very next season in
1980–81, and his first season proved to be his most productive. making him the youngest Rangers player to score in their NHL debut at 19 years and 195 days. His record was surpassed by
Lias Andersson in 2018, who was 19 years 164 days old. Allison finished the season as the Rangers' leader in
rookie scoring, and established team records for rookie assists (38) and points (64), although the records were surpassed the following season by
Mark Pavelich. For only the second time he played a full NHL season. By this point in his career, knee injuries had made Allison adjust his playing style to be more of a defensive player, often playing killing penalties, and less of an aggressive forward. In spite of this, he still was a strong contributor for the Maple Leafs in the 1986–87 NHL Playoffs. After playing three more partial seasons with the Kings, Allison retired from the NHL after the
1989–90 NHL season. ==Post-NHL career==