During his four-year major junior career, Gallagher received Western Hockey League (WHL) West First All-Star Team honors twice (2010–11 and 2011–12) and became the Vancouver Giants' all-time leading goal- and point-scorer.

The following season, Gallagher improved to 81 points over 72 games, ranking second among Giants players behind Craig Cunningham, while his 41 goals were a team high.

Overall, Gallagher registered 21 points (11 goals and 10 assists) in 16 postseason games, ranking second in team-scoring and fifth across the league,[4] as Vancouver was eliminated by the Tri-City Americans.

[5] During the playoffs of his draft eligible season, Gallagher was selected as the Male Youth Athlete of the Year for his hometown of Delta, British Columbia.

[10] Appearing in his second training camp with the Canadiens leading up to the 2011–12 season,[11] Gallagher was signed to a three-year, entry-level contract upon return to his junior squad.

[15] Following return to the lineup in late January,[10] he proceeded to break both the Giants' record for all-time goals and points set by Adam Courchaine seven years prior.

[18][19] Over the course of his junior career, Gallagher had earned a reputation as a fast-skating scorer who plays with energy and aggression, making him adept in both offensive and defensive situations.

[1] In his first professional season, Gallagher was assigned to the Canadiens' American Hockey League (AHL) affiliate, the Hamilton Bulldogs, due to the ongoing NHL lockout at the time.

[20] After the reacquisition of Michael Ryder by the Canadiens in February 2013, Gallagher switched from jersey number 73 to 11 to accommodate the veteran forward, who had worn 73 throughout his NHL career.

[22] He ended his rookie campaign with a total of 15 goals and 13 assists in 44 games, establishing himself as a key member of Montreal's offence, often playing on the Canadiens' first line.

[30] Gallagher ended the regular season with a career-high 54 points and was nominated for the King Clancy Memorial Trophy as a player who best exemplifies leadership qualities and community contributions.

On June 24, Gallagher had an assist on Artturi Lehkonen's semifinal series winner in Game 6 overtime against the Vegas Golden Knights, sending the Canadiens to their first Stanley Cup Finals in 28 years.

"[38] Finishing with just seven goals and 17 assists, Gallagher would later say that the main consolation of his worst season production wise to date was a four-month off-season that would enable him to recover his health and strength by working with his father Ian.

[47] In December 2010, Gallagher was invited to the annual selection camp for the Canadian national junior team,[48] but failed to make the roster after being amongst the initial cuts.

[50] In the last contest of the preliminary round, he was named his country's player of the game after recording a game-high seven shots on goal in a 3–2 win against the United States.

[55] In April 2016, Gallagher was added to the national senior team for the 2016 IIHF World Championship[56] where he scored two goals and three assists for a total of five points in ten games en route to a gold medal victory.

[61] He has three siblings: sisters Erin, a senior cost accountant at Stemcell Technologies in Vancouver,[62] and Breanne, a student-athlete who plays soccer at the University of Calgary, as well as a brother, Nolan, who is a member of the Burnaby Fire Department.