Thompson made an immediate impression on the Vegas Golden Knights when given the opportunity to become the No. 1 goalie to start the 2022-23 season after injuries to Robin Lehner and Laurent Brossoit. He began 8-2-0 to tie Marc-Andre Fleury (2017-18) for the most wins through 10 games in a season in Golden Knights history. He was also selected to represent the Golden Knights in the 2023 Honda NHL All-Star Game.

He was traded to the Washington Capitals by the Golden Knights on June 29, 2024, for third-round picks in the 2024 and 2025 NHL Drafts. He made 24 saves against his former team in his Capitals debut, a 4-2 win at Capital One Arena on Oct. 15, and signed a six-year, $35.1 million contract with Washington on Jan. 27. Thompson helped the Capitals rank first in the NHL in goals-against per game (2.37), and first in the NHL standings with a .724 points percentage (33-11-5) at the time of the signing, and was named the NHL's First Star for the week ending Jan. 19 after going 3-0-0 with a 0.33 GAA, .984 save percentage (61 saves on 62 shots) and two shutouts to lift Washington back atop the League.

Thompson's 39 saves in a 2-0 win against the Carolina Hurricanes at Capital One Arena on Dec. 7, 2025, made him the 17th goalie in NHL history to reach 100 wins in 170 games or fewer. The milestone came in his 167th game, third-fewest among active goalies behind Igor Shesterkin (159) and Matt Murray (166). He won a silver medal for Team Canada at the Olympic Winter Games Milano Cortina 2026.

Thompson went undrafted following four seasons with Brandon of the Western Hockey League. He attended Brock University to play in a Canadian university league, U Sports, which provides opportunities to Canadian Hockey League and Canadian Junior Hockey League graduates. He went 18-6-0 with a 2.22 goals-against average and .934 save percentage and was named U Sports rookie of the year and goalie of the year in 2018-19. He signed a two-year, entry-level contract with Vegas on July 13, 2020, and a three-year contract Jan. 30, 2022.

Though Thompson lost his first NHL start, 3-2 to the Nashville Predators on Jan. 4, 2022, he went 10-5-3 with a 2.68 GAA and .914 save percentage in 19 games (17 starts), including his first NHL shutout March 30. The strong finish came after he won the 2021 Aldege 'Baz" Bastien Memorial Award as the American Hockey League's outstanding goaltender by going 16-6-1 with a 1.96 GAA and a .943 save percentage for Henderson.