Jost made his NHL debut with the Avalanche during the 2016–17 season after the Fighting Sioux fell to Boston University in the first round of the 2017 NCAA Division I Men's Ice Hockey Tournament.
He spent the following 5 seasons within the Avalanche organization moving between their American Hockey League (AHL) affiliate, the Colorado Eagles, and the NHL level.
During his sixth season with the Avalanche, Jost was traded to one of their division rivals, the Minnesota Wild, where he played briefly before being waived and claimed by Buffalo.
[5] In spite of his high selection, Jost decided to play with the Okanagan Rockets of the British Columbia Major Midget League to retain his NCAA eligibility.
[6] In his first and only season with the Rockets, he led the team in scoring with 44 goals and 88 points to help them claim the BC Hockey Major Midget League (BCMML) Championship.
[17] As promised, Jost immediately began his collegiate career in the 2016–17 season, quickly adapting to the Fighting Hawks in assuming first-line responsibilities.
He finished his freshman season placing second amongst North Dakota in scoring with 16 goals and 35 points in 33 games, earning a selection to the NCHC All-Rookie Team.
[19] Jost continued to help the Fighting Hawks advance to the first round of the 2017 NCAA Division I Men's Ice Hockey Tournament, where they eventually lost to Boston University.
[21] Jost joined the Avalanche immediately to help close out the franchise's worst season in Denver, making his NHL debut in a 2–1 shootout victory over the St. Louis Blues on March 31, 2017.
[28] His play remained stagnant throughout the season and he was reassigned to the Avalanche's newest AHL affiliate, the Colorado Eagles, in January after recording six goals and nine assists in 43 games.
[34] On October 18, 2019, Jost recorded his first career NHL hat-trick in a 6–2 win over the Tampa Bay Lightning to extend the team's point streak to eight games.
[41] Featuring in a bottom six role, Jost helped the Wild to a 16-3-2 record through 21 appearances, including scoring the game-winning goal against his former club, the Colorado Avalanche, in the final regular season game on April 29, 2022.
[47] He made his debut with the Sabres, featuring in a bottom six role and helping Buffalo end an eight game winless streak in a 7-2 victory over the Montreal Canadiens on November 22, 2023.
As a free agent from the Sabres, Jost opted to continue his career in the Eastern Conference, securing a league-minimum one-year, $775,000 contract with the Carolina Hurricanes on July 1, 2024.
[54] Prior to his second season with the Penticton Vees, Jost and teammate Dante Fabbro were named to Canada's Under-18 to compete at the 2015 Ivan Hlinka Memorial Tournament.
[57] Jost captained Canada at the 2016 IIHF World U18 Championships in Grand Forks, North Dakota, where he led the tournament in scoring with 15 points in seven games.
[62] On May 10, 2019, Jost was again a late inclusion to Team Canada at the 2019 IIHF World Championship, joining the squad following the Avalanche's second round defeat in the post-season.