[4][3] Thompson spent the next three seasons with Brandon, posting a career .905 save percentage and 3.36 goals against average with a 63–41–10 record, and helping the team to a WHL Championship in 2016.

[7][8] After the conclusion of the Badgers' season, Thompson joined the Adirondack Thunder of the ECHL on an amateur tryout contract in March 2019.

[3][15][10] On July 13, 2020, Thompson signed a two-year, entry-level contract with the Vegas Golden Knights of the National Hockey League (NHL).

[20][21] On March 11, Thompson made his NHL debut against the Minnesota Wild in relief of Marc-André Fleury, playing eight minutes and stopping both shots he faced in a 4–3 loss.

[33] Thompson then recorded his first shutout of the season on October 13, stopping 27 shots as the Golden Knights defeated the Chicago Blackhawks 1–0.

[37][38] Similarly owing to his strong start, Thompson was initially considered a contender for the Calder Memorial Trophy as the NHL's best rookie.

[39][40] Thompson's rookie year was then cut short just after the All-Star Break, as he left early in a 5–1 victory over the Minnesota Wild on February 9, after suffering a lower-body injury.

[43] In his absence, the Golden Knights variously relied on Brossoit, Adin Hill, fellow rookie Jiří Patera, and the newly-acquired Jonathan Quick.

[54] After a 3–2 victory over the Los Angeles Kings on December 28,[50] Thompson started the 2024 Winter Classic for the Golden Knights on January 1, 2024, culminating in a 3–0 defeat to the Seattle Kraken.

[68] Subsequently, on June 29, the Golden Knights traded Thompson during the 2024 NHL entry draft to the Washington Capitals in exchange for two third-round picks.