Coincidentally, teammate Leonard Floyd also injured his hamstring at the combine and was unable to perform the three-cone and short shuttle.

Fellow Georgia linebacker and teammate, Leonard Floyd, was selected in the first round (ninth overall) by the Chicago Bears.

[16] He competed with Trevor Reilly, Lorenzo Mauldin, and Deion Barnes throughout training camp for the one of the jobs as starting outside linebacker.

[18] On September 25, 2016, Jenkins made his professional regular season debut and first career start, recording five combined tackles in a 24–3 loss to the Kansas City Chiefs.

During a Week 14 matchup against the San Francisco 49ers, he recorded four combined tackles and was credited with a half a sack on Colin Kaepernick in the Jets' 23–17 overtime victory.

[19] The next game, Jenkins collected five combined tackles and made his first career solo sack on Miami Dolphins quarterback Matt Moore, as the Jets lost 34–13.

[20] Jenkins finished the 2016 season with 41 combined tackles (23 solo), 2.5 sacks, a forced fumble and two passes defensed in 11 starts and 14 games.

On November 2, 2017, he earned two solo tackles, sacked Bills quarterback Tyrod Taylor twice, and forced the first fumble of his career, as the Jets won 34–21 on Thursday Night Football.