[8] For his efforts, Gregory was named a 2013 first-team All-Big Ten selection and rewarded with Nebraska's Defensive MVP.

However, in the season opener against New York Giants (three quarterback pressures in only 18 snaps), he suffered a high ankle sprain in the fourth quarter that forced him to miss the next four games.

[25] On September 29, Gregory was reported to have failed a second drug test, just after leaving an undisclosed treatment facility earlier that month, and was removed from the team's roster.

His year-long suspension was not in place at the time, so he was able to make his 2016 season debut, while the Cowboys released DE Zach Moore for Gregory.

[30] In the game, he told the coaching staff he was able to play through an oblique strain he suffered in the first quarter,[31] and went on to post two tackles and one quarterback hurry.

With the team suffering multiple injuries along the defensive line, he started in the last game of the season, a 27–13 loss to the Philadelphia Eagles.

)[33] Despite the possibility that the NFL would delay the appeal hearing for his latest suspension and allow him to play in the postseason, the meeting was held on January 3, 2017.

[38] On August 30, he met with the NFL's chief medical director, in what was reported to be a proactive meeting, to discuss his treatment and progress.

[41] On February 26, 2019, Gregory was suspended indefinitely by the NFL, for again violating the league's substance abuse policy, as well as reneging on the terms of his conditional reinstatement, from an incident that occurred on New Year's Day 2019.

[43] However, this extension was later blocked due to the terms of the 2020 collective bargaining agreement,[44] as well as the league ruling that players under suspension cannot be given new contracts.

[45] The Cowboys had lost sack leader Robert Quinn to the Chicago Bears in the off-season and needed a player like Gregory to fill that spot.

In Week 12, on November 26 (Thanksgiving), he recorded his first career multi-sack game, with two sacks on quarterback Alex Smith during their 41–16 loss to the Washington Football Team.

He went on to play in seven games, racking up 5 sacks (tied for team lead with fellow LB Micah Parsons), 10 combined tackles, 3 tackles for loss/"stuffs," 12 quarterback hits, 20 quarterback pressures (led team), 2 forced fumbles and one un-related fumble recovery.

However, he suffered a calf injury during practice before Week 10 and was placed on injured reserve on November 11, being expected to miss three games.

On December 12, against the Washington Football Team, he recorded a sack, a forced fumble, and his first career interception, on a pass that he both deflected at the line and caught, returning it for 12 yards.

[54][55] He finished the 2021 season with six sacks, 19 total tackles, one interception, one pass defended, and three forced fumbles, playing in 12 games with 11 starts.

[57][58] He suffered a knee injury in the fourth quarter of their Week 4 game against the Las Vegas Raiders, and was placed on injured reserve on October 4.

[60] He was to be suspended for one game on December 26, following a post–game fight with Los Angeles Rams guard Oday Aboushi after Denver lost 51–14.

Following their win over the Bears, the Broncos' new head coach, Sean Payton, had noticed that Randy's younger teammates, LB Nik Bonitto (2.5 sacks and a forced fumble in Week 4) and LB Jonathon Cooper (returned Bonitto's forced fumble for a touchdown in the Week 4 game), had been playing more effectively than Gregory as of late, prompting the team to part ways with him.