Moncrief played college football for the Mississippi Gulf Coast Bulldogs in 2012 and 2013, the Auburn Tigers in 2014 and the Oklahoma State Cowboys in 2015 and 2016.

[1] Moncrief was signed by the Saskatchewan Roughriders of the CFL on June 3, 2017, and played in his first professional football game on August 13, 2017.

On January 10, 2020, Moncrief signed a reserve/future contract with the Las Vegas Raiders of the National Football League (NFL).

[4] Moncrief signed with the Los Angeles Rams on August 25, 2020.

[15] He played in 14 regular season games where he recorded 50 defensive tackles, three sacks, and one interception.