During his four-season tenure with the Red Deer Rebels in the Western Hockey League (WHL), he set a new franchise record for most assists.

[1] In spite of recording 41 points in 33 games during the 2012–13 AMHL season, he was overlooked in the 2013 Western Hockey League (WHL) Bantam draft being too slight.

[1] In his rookie season with the team, he helped lead them to the 2016 Memorial Cup against the London Knights[3] and earned a final ranking of 104th overall by the NHL Central Scouting Bureau.

[9] By June 1, 2018, the Sabres were unable to sign Hagel to a contract and relinquished their rights to him, allowing him to become eligible for the 2018 NHL Entry Draft.

[15] After the Rebels were knocked out of the 2019 WHL playoffs, Hagel joined the Blackhawks American Hockey League affiliate, the Rockford IceHogs, for eight games and recorded one point.

[19] As a restricted free agent with the Blackhawks following his breakout 2020–21 season, Hagel was re-signed to a three-year, $4.5 million contract extension on August 6, 2021.

[22] In the 2023 Stanley Cup playoffs, he posted 1 goal and 5 points in a six-game first round exit to their Atlantic Division rival Toronto Maple Leafs.

[24] Hagel's success in the 2020–21 NHL season saw him earn his first invitation to represent Canada internationally, joining the senior national team for the 2021 IIHF World Championship.

[26] Following the Tampa Bay Lightning's ouster in the first round of the 2024 Stanley Cup playoffs, Hagel again joined Team Canada for the 2024 IIHF World Championship.

At the start of the 2018 Junior A season, he planned to pursue a college education and become a teacher if he did not receive an NHL contract by December of that year.

Since joining the Tampa Bay Lightning, Hagel has been actively involved in the NHL’s Hockey Talks initiative, which promotes mental health awareness.