He competed for Lake Ginninderra in the Australian National High School Basketball Championships in 2013,[8][9] helping them win the title.

[15] He made his NBA debut in the Jazz's season opener on 29 October, scoring five points in 9½ minutes off the bench in a 104–93 loss to the Houston Rockets.

He helped the Jazz to a 24–17 record as a starter and was selected to compete in the 2015 Rising Stars Challenge during the NBA's All-Star Weekend in New York.

[19] In August 2015, Exum sustained a tear of the anterior cruciate ligament (ACL) in his left knee while playing for Australia in Slovenia.

[30] On 7 January 2019, he was ruled out for "a couple of weeks" due to an ankle sprain that he suffered two days earlier against the Detroit Pistons.

[34] On 24 December 2019, Exum was traded, alongside two second-round picks, to the Cleveland Cavaliers in exchange for Jordan Clarkson.

Partizan ended the 2022–23 season by lifting the ABA League championship trophy, after 3–2 score against Crvena zvezda in the Finals series.

[43] On 12 December 2023, Exum scored a season-high 26 points with a career-high seven made three-pointers in a 127–125 win over the Los Angeles Lakers.

2013 also marked Exum's debut for the senior national team, playing against New Zealand at the 2013 FIBA Oceania Championship.

[48] In the bronze playoff, he scored or assisted on 13 of Australia's points in the pivotal 20–8 run that turned a five-point lead into a 17-point advantage (105–88) with just over a minute remaining.

[50] His father, Cecil, played college basketball at the University of North Carolina and won an NCAA championship in 1982, a team which featured Michael Jordan and James Worthy.