Morris played for the Bowling Green Falcons for four seasons. He finished his collegiate career with 125 receptions for 1,529 yards and 13 touchdowns in 40 games played.[4][5] As a junior in 2019, Morris caught a career high 10 receptions for 92 yards against Notre Dame.[6] During the season, Morris was converted from wide receiver to tight end.[7] He led the team with 55 receptions, 649 receiving yards, and four touchdown catches, being named Second Team All-MAC. The following COVID-shortened season, he played all five-games where he earned First Team All-MAC, becoming the first Bowling Green tight end named since 1991.[8]
Morris was signed by the Buffalo Bills as an undrafted free agent on May 1, 2021.[11][5] He was waived during final roster cuts on August 31, 2021, but was signed to the team's practice squad the next day.[12][13] Although on the practice squad for most of the year, Morris was elevated to the active roster on October 26, 2021, for the team's Week 9 game against the Jacksonville Jaguars but did not play during the game.[14] After the Bills were eliminated in the Divisional Round of the 2021 playoffs, he signed a reserve/future contract on January 24, 2022.[15]
Following the 2022 NFL preseason, Morris was named to the official 53-man roster listed as the backup tight end to Dawson Knox to begin the season, edging out former Buccaneer's first round pick O.J. Howard for a roster spot.[16][17] On September 19, 2022, the Bills hosted the Tennessee Titans on Monday Night Football where Morris would make his National Football League debut. Morris finished the game with 28 offensive and 19 special teams snaps. Morris would haul in his first NFL reception from quarterback Josh Allen for six yards during the Bills 41–7 victory.[18] In Week 5 against the Pittsburgh Steelers, Morris earned his first career start. Morris would have a career high three catches and 39 receiving yards in a 38–3 victory.[19] In Week 15 against the Miami Dolphins, Morris would catch his first career NFL touchdown pass. In the first quarter, Allen would connect with Morris on a 14-yard touchdown. The Bills won the game 32–29, on a game winning 25-yard field goal from kicker Tyler Bass as time expired.[20] He appeared in 14 games and started one as a rookie. He had eight receptions for 84 yards and a touchdown on the season.[21]
Entering the 2023 season, Morris was listed as the third-string tight end, remaining primarily on special teams.[22] On October 15, 2023, Morris caught the go-ahead touchdown pass to lift the Bills to a 14–9 win over the New York Giants.[23] After the game, Morris was praised by Bills fans and head coach Sean McDermott for helping the team win despite having an injured ankle, along with other injuries on the team.[24] The following two weeks, Morris sat out due to his ankle injury.[25][26] He appeared in 15 games in the 2023 season, with two receptions, 26 yards, and one touchdown.[27] On March 8, Morris signed a one-year contract with the Bills.[28]
Entering the 2024 season, Morris was listed as the third-string tight end for the second year in a row.[29]