Growing up, Frost would accompany his father Andy, and sister Marley to Toronto Maple Leafs games, where he developed a passion for hockey.

This culminated in two consecutive seasons of Frost scoring 100 or more points, as well as an appearance for Canada at the 2019 World Junior Ice Hockey Championships.

The Flyers traded forward Brayden Schenn in exchange for the draft selection that went to Frost, and he signed a contract with the team in August 2017.

He began the 2020–21 NHL season as a bench player for the Flyers, but his opportunity to fill in for an injured Sean Couturier was derailed by a season-ending shoulder injury.

His father Andy, meanwhile, served as the public address announcer for the Toronto Maple Leafs of the National Hockey League (NHL) from 1999 to 2016.

[3] When Frost was 13 years old, he was physically smaller and less aggressive than many of his teammates, which led to his being cut from the elite 'AAA'-level minor ice hockey team in the region, the York–Simcoe Bantams.

[10] In addition to serving as the Greyhounds' top-line centre, Frost was on both the power play and penalty kill squads, posting 42 goals, 112 points, and a +70 plus–minus during the regular season.

[11] Frost was disappointed in his own playoff performance, however: he scored 10 goals and 19 assists in 24 games, but had a −4 plus–minus, and the Greyhounds were defeated in the finals by the Hamilton Bulldogs.

[1] After a groin injury limited Frost's performance during the Flyers' training camp, he was assigned to the Lehigh Valley Phantoms, Philadelphia's American Hockey League (AHL) affiliate, to begin the 2019–20 season.

[23] After only two games, however, Frost entered a 16-game drought during which his only points were four assists, and he was sent back to Lehigh on December 29 to clear room on the roster for Michael Raffl, who was coming off of the injured list.

[25] Frost played a total of 41 games with the Phantoms, recording 13 goals and 29 points in the process, before the AHL season was suspended and ultimately cancelled due to the COVID-19 pandemic.

[32] He scored 15 points in the first 16 games of the Phantoms' season before being called up to the Flyers on November 24 to fill a roster that had been hindered by injuries to Kevin Hayes and Derick Brassard.

[33] During the 2024–25 season, his sixth with the Flyers, Frost was traded along with Joel Farabee to the Calgary Flames in exchange for Andrei Kuzmenko, Jakob Pelletier and two draft picks on January 30, 2025.