USHL Going undrafted into the
United States Hockey League (USHL), Morris made the
Chicago Steel roster following tryout camp in 2013. In his senior year of high school, Morris moved to
Bartlett, Illinois, to play with the Chicago Steel and lived with teammate Robby Jackson. During that season, Morris committed to play NCAA college hockey for the
University of Notre Dame Fighting Irish. Although the final rankings from the
NHL Central Scouting Bureau ranked Morris 15th for North American goaltenders, he went undrafted in the
2015 NHL entry draft. In his second season with the Black Hawks, Morris was named an alternate captain. By December 2015, Morris had a 7–4–2 record and was in the league's top
goals-against average and
save percentage. As a result, he was selected to the USHL/NHL Top Prospects Game. While playing in the tournament, Morris became the fifth goaltender to post a shutout at the USHL/NHL Top Prospects Game. On March 22, 2016, Morris set a new Black Hawks record with his seventh regular season shutout. His seventh shutout came in a 5–0 win over his former team, the Chicago Steel. A month later, Morris was voted as the Waterloo Black Hawks MVP. During the summer, Morris was invited to the
Anaheim Ducks Development Camp Scrimmage as a college invite before joining Notre Dame for his freshman year.
Collegiate Enrolled in the
Mendoza College of Business, Morris made his Notre Dame collegiate debut on October 7, 2016, against
Arizona State. 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. 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. On February 9, 2018, Morris made 31 saves in a 2–1 victory over
Ohio State to help the Fighting Irish win the Big Ten regular-season championship and qualify for the
2018 Big Ten men's ice hockey tournament in their first year in the Big Ten conference. Ohio State and Notre Dame met again during the post-season in the Big Ten Championship Finals. Before the Championship Finals, Morris was named
Big Ten Goaltender of the Year,
Big-Ten Player of the Year,
First Team All-Big Ten, and a
Hobey Baker Award top 10 finalist. On March 17, the Fighting Irish beat Ohio State in overtime to clinch the Big Ten Conference Tournament championships and qualify for the
2018 NCAA National Championship tournament. Morris was named
Big Ten Tournament MVP and selected for the
Big Ten All-Tournament Teams due to his play. He then helped the Fighting Irish qualify for the
2018 NCAA National Championship Final by defeating the
Michigan Wolverines in the National Semifinals. After Notre Dame advanced to the National Championship Finals, Morris was awarded the
Mike Richter Award, becoming the first Notre Dame goaltender to receive the award. Notre Dame played the
2018 National Championship game against Minnesota Duluth, losing 2–1 with Morris making 33 saves. Although Notre Dame lost, Morris was named an
AHCA First Team All-American. Leading up to the
2018–19 season, Morris was named a unanimous selection on the Big Ten Preseason Watch List. In the annual
Ice Breaker Tournament, Morris posted a 22 save shutout in a 3–0 win over
Providence Friars to win the Championship. His second shutout of the season came on December 31 in a 4–0 win over
Boston College. This shutout helped earn him Big Ten First Star of the Week honors. On January 16, 2019, Morris was named a nominee for the Hobey Baker Award. 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. On March 12, Morris was again named a finalist for Big Ten Goaltender of the Year and was later selected for the
All-Big Ten Second Team. 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. After the game, Morris was named the tournament's Most Outstanding Player and selected for the Big Ten All-Tournament team. 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. On April 12, Morris committed to return to Notre Dame for his senior year, citing "unfinished business" as his reason. He was subsequently named an
alternate captain on September 19 alongside Tory Dello, becoming only the second goaltender to become an
alternate captain under head coach Jeff Jackson. However, before he could begin the collegiate season, Morris was injured during training camp which forced his season debut to be delayed. He eventually made his season debut on October 26 against Lake Superior State where he made 29 saves in the 6–4 win. By December, Morris was named a Big Ten First Star of the Week for recording his ninth career collegiate shutout while facing 37 shots. On February 21, in his 100th collegiate game, Morris recorded his 56th win in a 2–1 victory over the
Michigan Wolverines.
Professional As collegiate hockey was suspended due to the
COVID-19 pandemic in North America, Morris signed his first professional contract with the
Rockford IceHogs of the
American Hockey League (AHL) on October 12, 2020. As an impending restricted free agent with the Blackhawks, Morris was not tendered a qualifying offer by the rebuilding Blackhawks, and was released to free agency on 12 July 2022. 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. At the conclusion of his contract with the Wolves, Morris opted to continue his professional career in the ECHL, signing a one-year contract for the
2023–24 season with the Kansas City Mavericks on October 19, 2023. On December 11, 2023, the
Coachella Valley Firebirds of the
American Hockey League (AHL) signed Morris to a professional tryout agreement (PTO). ==International play==