Irving grew up in Compton, California, but moved to San Jacinto, California as a youth and attended San Jacinto High School, where he played defensive tackle and tight end as a senior, recording 76 tackles (15 for loss), 7 sacks, 5 forced fumbles, 4 fumble recoveries, 19 receptions for 298 yards and 4 touchdowns.

[1] He finished his college career with 32 games (8 starts), 44 tackles (7.5 for loss), 3 sacks, one forced fumble, one interception returned for a touchdown, 8 passes defensed and 3 blocked kicks.

He suffered a left wrist fracture in the fifteenth game against the Buffalo Bills and was placed on the injured reserve list on December 30.

On October 16, 2016, in a 30–16 win against the Green Bay Packers Irving was named NFC Defensive Player of the Week, when he forced three fumbles, recovering one, had a sack, and batted down a pass.

Irving's play also led to Tampa Bay personnel and coverage changes that created opportunities for other Cowboys players, including rookie defensive tackle Maliek Collins sacking Winston with one minute left to play, which set up a game-sealing interception by cornerback Orlando Scandrick.

[9] On May 23, it was announced that Irving would be suspended four games due to violating the league's performance enhancing drugs policy.

Despite missing the first four games because of his suspension, and the final four because of a concussion, Irving still accrued seven sacks (second on the team), 19 quarterback pressures, 12 tackles (3 for loss), 6 passes defensed and one forced fumble.

[13] On June 15, it was announced that due to violating the NFL's Policy and Program for Substances of Abuse, Irving would again be suspended for the first four games of the regular season.

[14] The Cowboys placed Irving on the reserve/did not report list on July 25 to start training camp, as he dealt with his off-field issues.