Quinn previously played professionally for Paris FC in France's top league Division 1 Féminine (D1F), Vittsjö GIK in the Swedish Damallsvenskan, as well as Washington Spirit and Seattle Reign in the NWSL.

[5] Quinn's father, Bill, was a collegiate rugby player and their mother, Linda, played college basketball.

Raised with their three sisters in a sporting family in Toronto, Quinn began playing soccer with a club team at the age of six.

Quinn attended Havergal College, an independent school where they played varsity volleyball and basketball and earned academic honours all four years.

[6] As a redshirt senior in 2017, Quinn earned Atlantic Coast Conference (ACC) Midfielder of the Year honors (the first Duke player to do so) and was a Hermann Trophy semifinalist.

[12] Wanting to play in Europe ahead of the 2019 FIFA Women's World Cup in France,[13] Quinn signed with Division 1 Féminine (D1F) club Paris FC.

[16] In July 2019 (following the FIFA Women's World Cup in France), Quinn returned to the NWSL in the United States and signed with Reign FC based in Tacoma, Washington.

[11] The club finished in fourth place with a 10–6–8 record and earned a berth to the NWSL Playoffs[19] They were defeated 4–1 by eventual champions North Carolina Courage during the semifinal.

[15][11] On 7 March 2014 at the age of 18, Quinn made their senior national team debut in a 3–1 win against Italy in the 2014 Cyprus Cup.

[29] On 16 February 2016, they scored a hat-trick against Guatemala in a 10–0 win in the group stage of the 2016 CONCACAF Women's Olympic Qualifying Championship.

[30] In June 2016 while still playing collegiate soccer for Duke, Quinn was named to the roster for the 2016 Summer Olympics where Canada won bronze.

[31][32] During the team's first match of the tournament, Quinn subbed in the 23rd minute helping Canada shutout Australia with a 2–0 win.

[44] During the team's second group stage match, Quinn was a starting midfielder and scored a goal in the 56th minute helping Canada win 12–0 against Cuba.

[55] During the team's first group stage match, Quinn subbed into the right midfielder position in the 62nd minute and helped the Canada win 11–0.

[57] After defeating Costa Rica 1–0 in the semi-final and securing a post at the Olympics,[58] During the final against the United States, Quinn was a starting midfielder.

[60] Quinn played 72 minutes of the team's first group stage match against hosts Japan which resulted in a 1–1 draw and became the first openly transgender as well as first non-binary athlete to compete at the tournament.

"[61] Quinn played 29 minutes of Canada's second group stage match against Chile helping the team win 2–1.

[62] After tying Great Britain 1–1 with Quinn playing as a starting midfielder,[63] Canada finished second in Group E and advanced to the quarterfinals.

[70] The 2023 FIFA Women's World Cup proved to be a major disappointment for Canada, who failed to advance past the group stage.

Quinn played for almost the entirety of the team's three matches, only being substituted in the closing minutes of their 4–0 loss to Australia in order to give newcomer Olivia Smith an appearance.

[71][72] In 2020, Quinn came out as non-binary and transgender (using gender-neutral pronouns) and changed their name by adopting their prior surname as a mononym.

[73] They were permitted to continue playing professional women's soccer on the basis of their sex assigned at birth, rather than gender identity.