Following success in the United States Hockey League with the Chicago Steel and Waterloo Black Hawks, Morris joined the University of Notre Dame in the Big Ten Conference (B1G).
[2][4] Going undrafted into the United States Hockey League (USHL), Morris made the Chicago Steel roster following tryout camp in 2013.
[5][6] In his senior year of high school, Morris moved to Bartlett, Illinois, to play with the Chicago Steel and lived with teammate Robby Jackson.
[2] In his first year with the Steel, Morris finished the season with a 19–6–3 record and a .937 save percentage and graduated from South Elgin High School.
[18] At the conclusion of the 2016–17 season, Petersen signed a professional contract, ending his collegiate career and leaving an opening for Morris to become the new starter.
[19] After beginning his sophomore season, he split his time in net with freshman Dylan St. Cyr, Morris gained the starter position and helped Notre Dame win 16 games in a row.
[18] On December 6, 2017, Morris was named the Hockey Commissioners’ Association (HCA) Player of the Month for November after he posted an 8–0–0 record with three shutouts and a nation-leading .969 save percentage.
[34] Morris helped the Fighting Irish qualify for the 2019 Big Ten men's ice hockey tournament where he posted back-to-back shutouts to defeat the Michigan State Spartans in the quarterfinals.
[37] On March 23, 2019, Morris and the Notre Dame Fighting Irish won their second Big Ten Conference Tournament championship title after a 3–2 win over Penn State.
[39] However, in the second round of the 2019 NCAA Division I Men's Ice Hockey Tournament against the UMass Minutemen, Notre Dame lost 4–0 and was eliminated from the competition.
[44] By December, Morris was named a Big Ten First Star of the Week for recording his ninth career collegiate shutout while facing 37 shots.
[48] Morris opted to continue in the AHL, later signing a one-year contract for the 2022–23 season with the Chicago Wolves, the primary affiliate to the Carolina Hurricanes, on July 26, 2022.
[50] On December 11, 2023, the Coachella Valley Firebirds of the American Hockey League (AHL) signed Morris to a professional tryout agreement (PTO).