He played college football for the Iowa Hawkeyes and was selected by the Cleveland Browns in the third round of the 2014 NFL draft.

In addition to football, Kirksey participated in track & field at Hazelwood East, where he competed in relays and jumping events, helping his team win the state championship as a junior.

[4] Throughout the week, leading up to the game, Kirksey impressed scouts and team representatives during practice by displaying his athleticism, explosiveness, and ability to finish plays.

He had an impressive performance playing for former Atlanta Falcons head coach Mike Smith's North team.

[8] On March 24, 2014, Kirksey participated at Iowa's pro day, along with C. J. Fiedorowicz, Anthony Hitchens, James Morris, and nine other prospects.

Representatives and scouts from 28 NFL teams attended as he performed all of the combine and positional drills and was able to increase his vertical by four inches (36").

[9] At the conclusion of the pre-draft process, Kirksey was projected to be a fourth or fifth round pick by the majority of NFL draft experts and scouts.

[14] Throughout training camp, Kirksey competed against Craig Robertson for the job as the starting right inside linebacker.

[15] Head coach Mike Pettine named him the backup right inside linebacker to Robertson to begin the regular season.

Kirksey started over Robertson during a Week 11 matchup against the Houston Texans and tied his season-high of nine combined tackles in Cleveland's 23–7 loss.

He finished his rookie season with 81 combined tackles (47 solo), two sacks, two pass deflections, and a forced fumble in eight starts, 16 games, and 343 defensive snaps.

[23] Kirksey was slated to be the starting inside linebacker after Robertson departed during free agency to the Saints.

He started the Browns' season-opener at the Philadelphia Eagles and recorded six combined tackles and sacked Carson Wentz during 29–10 loss.

In Week 17, Kirksey recorded 12 combined tackles and sacked Roethlisberger, for his third time in his career, during a 27–24 loss at the Steelers.

Kirksey had an impressive season in 2016 and led the Browns with 148 combined tackles (96 solo), 2.5 sacks, and three pass deflections in 16 games and 16 starts.

[27] During a Week 2 matchup at the Ravens, Kirksey made nine combined tackles and sacked Joe Flacco as the Browns lost 24–10.

On November 19, 2017, Kirksey collected 14 combined tackles and sacked Jaguars quarterback Blake Bortles in a 19–7 loss.

[40] In Week 11 against the Indianapolis Colts, Kirksey led the team with 11 tackles and recorded his first interception as a Packer off a pass thrown by Philip Rivers during the 34–31 overtime loss.

[41] In Week 16 against the Titans on Sunday Night Football, Kirksey sacked and intercepted Ryan Tannehill once each, also recording a solo tackle for loss and a pass deflection during the 40–14 win.