In Monroe's career with Nicholls, he was a three-year starter where he totaled 102 tackles, 28 pass deflections, and an interception.[4] After the conclusion of the 2021 season, Monroe entered the NCAA transfer portal.[5]
Tulane
Monroe decided to transfer to play for the Tulane Green Wave.[6][7] In week one of the 2022 season, Monroe recorded his first interception with Tulane in a win over UMass.[8] In the 2023 Cotton Bowl Classic, Monroe intercepted Heisman-winning quarterback Caleb Williams as he helped Tulane upset USC.[9] During the 2022 season, Monroe notched 49 tackles, eight pass deflections, and three interceptions.[10] For his performance in the 2022 season, Monroe was named first-team American-Conference.[11] Monroe finished the 2023 season with 48 tackles, three sacks, ten pass deflections, three interceptions, and a forced fumble.[12] For his performance on the year he was once again named first team American-Conference.[13] Monroe was invited to participate in the 2024 East-West Shrine Bowl, where he was named the game's Defensive MVP.[14]
Monroe signed with the New York Jets as an undrafted free agent on May 3, 2024.[16] He was waived on August 27, and re-signed to the practice squad.[17][18]