Clapp did not play as a true freshman in 2014 and chose to redshirt. In 2015, as a redshirt freshman, Clapp started all 12 games for the Tigers. He ranked third on the team in total snaps with 776 and knockdown blocks with 88, along with not allowing a sack all season.[2] He was named to the 2015 Southeastern Conference (SEC) All-Freshman team.[3]
As a redshirt sophomore in 2016, Clapp started 11 of 12 games, missing one due to injury. He played 648 snaps, had 58 knockdown blocks and did not allow a sack for the second straight season.[2] He was named to the 2016 All-SEC football team.[4]
In 2017, Clapp started all 13 games for the Tigers.[5] He was named to the All-SEC Football Team for the second year in a row.[6] After the season, he announced he was going to forgo his final year of eligibility and enter the 2018 NFL Draft.[7]
Clapp was drafted by the New Orleans Saints in the seventh round (245th overall) of the 2018 NFL Draft.[10] On May 10, 2018, Clapp signed his rookie contract with the Saints.[11] He made his NFL debut on December 17, 2018, against the Carolina Panthers as a substitute for Michael Ola.[12] Clapp saw action in 14 games during the 2019 season, starting three.[13]
On September 26, 2020, Clapp was waived by the Saints and re-signed to the practice squad on September 29.[14][15] Clapp spent much of the remainder of the 2020 season alternating between the active roster and the practice squad,[16][17][18][19][20][21][22][23] playing in several games in the middle of the season before being permanently added back to the active roster,[24] though he also spent time on the reserve/COVID-19 list during the postseason.[25][26]
Clapp re-signed with the Saints on April 20, 2021.[27] After starting the regular season on injured reserve,[28] Clapp was re-activated on October 2, spending the rest of the season alternating between the practice squad and active roster as with the previous year.[13][23] Clapp started three games in 2021, playing with the likes of Jameis Winston, Trevor Siemian, and Taysom Hill after spending his first three years with Drew Brees under center.[13]
On April 6, 2023, Clapp re-signed with the Los Angeles Chargers.[30] Following a season-ending health issue from starter Corey Linsley, Clapp was named the starting center in Week 4. He suffered a knee injury in Week 15 and was placed on injured reserve on December 18.[31]
On March 22, 2024, Clapp signed a one-year deal with the Buffalo Bills.[32] The move reunites Clapp with Bills offensive coordinator Joe Brady, who was an offensive assistant with New Orleans during Clapp's rookie season.[13]