Gavigan would start his career at the Nottingham Ice Hockey Club from the age of four. He would play within the Nottingham system all the way through until the 2016-17 season. He was named Captain of the Nottingham U15's in which he lead them to a league title and a promotion for his final season.
Gavigan would then make the move to the Sheffield Ice Hockey Academy for his U18 career and the start of his senior one too. In his time playing for the U18's, Gavigan would win the North League Championship and follow it up with a National Championship, scoring the winning goal in the final versus Okanagan Hockey Academy. Gavigan would again be named captain in his final season as a junior.
Following on from finishing his junior career, Gavigan would ice for the Sheffield Titans. Half way through the season, he was named captain for the team and lead them to a Playoff Semi-Final in their first ever season.
Since the 2022/23 season, he has iced for the Coventry NIHL Blaze which would see him collect four team awards in his two seasons. Most recently Best Defenseman and Players Player of the Year.