During his junior year, he had 111 tackles and 24+1⁄2 sacks, helping the Desert Vista Thunder to the Class 5A Division I title game.

[1] In Desert Vista's 21–20 victory over Chandler High School, Kennard suffered a torn anterior cruciate ligament in his right knee, causing him to miss the rest of the football season.

[4] Recruited by over forty schools nationwide, Kennard initially considered Arizona State, California, Florida, Miami, North Carolina, Oregon, Texas, UCLA, and USC.

[1][5] Kennard attended summer camps with USC following his sophomore and junior seasons in high school, and grew close to USC-commit Matt Barkley.

[10] In his true freshman year at USC, Kennard began the season as a backup defensive end, but by midseason was seeing key action primarily in pass rushing situations.

He made the 2009 Pac-10 All-Freshman first-teams by ESPN and Sporting News, and won USC's John McKay Award.

Kennard moved back to defensive end for the 2011 season, where he played in all twelve games, with five starts, and 29 tackles, including 4 for losses (with 2 sacks, one which resulted in a safety).

[11] On January 18, 2014, Kennard recorded two solo tackles as part of Romeo Crennel's West team that lost 23–13 to the East in the 2014 East-West Shrine Game.

On March 12, 2014, he participated at USC's pro day, but opted to stand on his combine numbers and only performed positional drills.

At the conclusion of the pre-draft process, Kennard was projected to be a fifth or sixth round pick by NFL draft experts and scouts.

[22][23] Head coach Tom Coughlin named Kennard a backup outside linebacker to begin the season in 2014, behind starters Jameel McClain and Jacquian Williams.

[29] He finished his rookie season in 2014 with 43 combined tackles (35 solo), 4.5 sacks, two forced fumbles, and a pass deflection in 12 games and six starts.

[32] On January 15, 2015, the New York Giants hired the Baltimore Ravens' former secondary coach Steve Spagnuolo to be their new defensive coordinator.

[34][35] Head coach Tom Coughlin named Kennard the starting strongside linebacker to begin the regular season, alongside J.T.

[36] In Week 2, he collected a season-high ten combined tackles (seven solo) and deflected a pass during a 24–20 loss to the Atlanta Falcons.

Kennard made his first career interception off a pass by Bills' quarterback Tyrod Taylor, that was originally intended for tight end Charles Clay, in the first quarter.

On December 28, 2015, the New York Giants officially placed Kennard on season-ending injured reserve due injuries to his foot and hamstring.

[39] Kennard finished the season with 58 combined tackles (37 solo), four pass deflections, and one interception in nine games and nine starts.

[45] Kennard recorded 61 combined tackles (40 solo), one sack, one pass defensed, and a forced fumble in 16 games and nine starts.

[47] Kennard finished the 2017 NFL season with 41 combined tackles (24 solo), four sacks, and two pass deflections in 15 games and 11 starts.

[49][50] On September 16, 2018, Kennard recorded four combined tackles and made two sacks on 49ers' quarterback Jimmy Garoppolo during a 30–27 loss at the San Francisco 49ers in Week 2.

[52] In week 12 against the Washington Redskins, Kennard recorded a strip sack on Dwayne Haskins which was recovered by teammate Tavon Wilson in the 19–16 loss.

[58] Kennard was voted the NFL Player Association representative by his teammates (NY Giants, Detroit Lions, AZ Cardinals) consecutively from 2016 – 2020.

He was selected to be one of USC's representatives at the 2011 APPLE (Athletic Prevention Programming and Leadership Education) Conference in Austin, Tex., designed to promote student-athlete health and wellness.