Jarry started with the Edmonton Oil Kings during the 2011–12 WHL season, playing 14 games with a 0.894 save percentage. In his second season with Edmonton, Jarry played 27 games, and led all goaltenders with a 0.936 save percentage and 1.61 goals against average. In the 2013 CHL Top Prospects Game, Jarry stopped all 16 shots at him to be named Team Cherry's Player of the Game, and the following season he was named to the 2013–14 WHL Eastern Conference First All-Star Team.
Displayed on Jarry's goalie mask are the Penguins of Madagascar playing pond hockey against Tom and Jerry, referencing the Pittsburgh Penguins and playing homage to his last name. Tom and Jerry was a nickname given to Jarry by previous teammate Kristian Pelss who died in 2013.
On April 7, 2015, Jarry was assigned to the Wilkes-Barre/Scranton Penguins. On April 9, 2016 Jarry was called up by Pittsburgh Penguins wearing #35 when goalies Marc-André Fleury and Matt Murray were both injured. He dressed for first two games of the playoffs for Pittsburgh, then was sent back to the minors when Murray returned from injuries. On May 19 he was recalled for rest of the season as emergency goaltender. Tristan Jarry did not qualify to be on the Cup, since he did not play for the Penguins in 2015–16 regular season or dress in the Stanley Cup Finals. He was given a Stanley Cup ring for his efforts.
Jarry played his first NHL preseason game on September 28, 2016 where he posted a 30 save shutout in a 2–0 victory over the Chicago Blackhawks. Despite an early-season injury to starting goalie Matt Murray, the Penguins returned Jarry to Wilkes-Barre for the start of the AHL season and instead signed Mike Condon as backup. With Jarry as the starting goaltender for the baby Penguins he posted career numbers in 45 games with 28 wins and a 2.15 goals against average, being named to the 2017 all-star game receiving the Harry "Hap" Holmes Memorial Award, and helping Wilkes-Barre finish with the best record in the regular season. Jarry was called up to the NHL on an April 9, and the next day, made his NHL debut, starting for the Penguins in a 3–2 loss to the New York Rangers on the final game of the regular season, in a game in which Magnus Hellberg also made his first NHL start. Due to an injury to Matt Murray, Jarry remained on the NHL roster as a backup to veteran Marc-André Fleury. Jarry dressed for 11 playoff games, until Murray return from injury. Penguins repeated as Stanley Cup Champions. Jarry received another Stanley Cup ring from the Penguins organization, despite only playing in one NHL game. Jarry did not dress in the finals, so he could not get his name on the cup.
Jarry won his first NHL game, and got his first NHL assist, on November 25, 2017 in a 5-2 win against the Tampa Bay Lightning. He then won his first NHL shutout six days later on December 1, 2017, in a 4–0 win against the Buffalo Sabres. On January 24, 2018, he was reassigned to the Wilkes-Barre/Scranton Penguins, when Matt Murray returned after missing the rest of the first half of the season due to the death of his father. He was recalled on February 4, 2018, replacing Casey DeSmith as backup. On February 26, Pittsburgh recalled DeSmith, once again switching with Jarry for the backup goaltender position. However, Jarry was recalled the very next day after Murray suffered a concussion the day prior.