Morse attended the University of Virginia, and played for the Cavaliers from 2016 to 2019. During the 2016 season, she started in all 21 games in which she played, scored two goals, and was selected for the All-ACC Freshman team. The following season, she competed in 22 matches, drawing the start in 21, tallied one assist, and was named to the ACC Women's Soccer All-Academic Team. In 2018 Morse played in 20 games, all of which she started, scored one goal, and was named to the ACC Women's Soccer All-Academic Team for the second time. Morse served as a co-captain of the Cavaliers alongside fellow senior Meghan McCool during the 2019 season, starting all 22 games, playing a team-leading 1,923 minutes on the back line, helping the team post 14 shutouts on the season, including 7 consecutive shutouts in ACC play, scoring the opening goal against the Florida State Seminoles women's soccer team in the semifinal game of the 2019 ACC Women's Soccer Tournament, and being selected for both the All-Region Second Team selection by United Soccer Coaches and the ACC Championship All-Tournament Team. On January 16, 2020, Morse was selected as the 19th overall pick in the 2020 NWSL College Draft by the Chicago Red Stars.
