[3] In 2016, Quinn made his car racing debut in the F4 British Championship, driving for Fortec Motorsport.

Quinn also made a one-off appearance in the BRDC British Formula 3 Championship that same year, scoring a podium at Donington with Lanan Racing.

However, midway through the season he was given the opportunity to make his debut in the Formula Renault Eurocup for his former F4 team Arden Motorsport.

[10][11] In May 2022, Velocity Racing Development and Arden International announced a collaboration which resulted in Quinn making a one-off appearance in the U.S. F2000 National Championship at the Indianapolis Motor Speedway.

[13][14] Quinn made his debut in sportscar racing at the start of 2023, competing in the 24 Hours of Daytona for the PR1/Mathiasen Motorsports outfit.

[15] With the team's amateur driver Ben Keating having scored pole position in the LMP2 category, Quinn, along with Paul-Loup Chatin and Nicolas Lapierre, finished the race in seventh place.

During the season, Quinn would join Chatin and Keating for the Michelin Endurance Cup rounds, helping them towards two podiums at Watkins Glen and Road Atlanta that earned the pair the overall LMP2 title.