Hargrave began attending South Carolina State in 2012. As a freshman in 2012, he finished with 45 tackles and 4.5 tackles for a loss. He was named a Freshman All-American.

On October 25, 2014, he tied an FCS record after finishing with a total of 6 sacks against Bethune-Cookman. He finished third among the FCS with 16 sacks as a junior in 2014 and was voted an Associated Press All-American.

In the 2015 season opener he made 6 solo tackles, 4.5 tackles for losses, and 2.5 sacks in a 35–7 victory against Arkansas-Pine Bluff. On September 16, 2015, he made 3 tackles and 2.5 tackles for a loss in a 36–0 shutout of Florida A&M. On October 3, 2015, he had a season-high 10 tackles and a sack in a loss to Furman. On October 24, 2015, Hargrave had one of his best games of the season, finishing with 6 solo tackles, 8 total tackles, 4 tackles for losses, forced a fumble, and had a season-high 3 sacks against Delaware State. In Week 11, he again had a season-high 3 sacks, 7 tackles, and 4 tackles for losses in a victory over Norfolk State. In his last career collegiate game he made a total of 4 tackles, 2 sacks, and a forced fumble in a win over Savannah State.

On January 23, 2016, Hargrave participated in the 2016 East–West Shrine Game and raised his draft stock with a good performance. Hargrave was invited to the NFL Scouting Combine and participated in all workouts and positional drills. At South Carolina State’s Pro Day, he stood on his combine numbers and only did positional drills. Representatives and scouts from 23 NFL teams attended his Pro Day and four defensive line coaches from the Cincinnati Bengals, Pittsburgh Steelers, Philadelphia Eagles, and Tennessee Titans also came to watch Hargrave, along with 14 other prospects. Although analysts and scouts gave him positive reviews for his motor, playmaking ability, quick footwork, athleticism, and strength they also criticized him for his short arms, stocky frame, small hands, lack of instincts, and also considered him a raw talent. At the conclusion of the pre-draft process, Hargrave was projected by many analysts as a third or fourth round selection. He was ranked as the 11th best defensive tackle prospect in the draft by NFLDraftScout.com.

On June 10, 2016, the Pittsburgh Steelers signed him to a four-year, $3.114 million rookie contract with a $693,000 signing bonus. Hargrave was the last player of the Steelers’ 2016 draft class to sign a contract with the Steelers.

He made his professional regular season debut during Pittsburgh Steelers’ season-opener at the Washington Redskins and helped them win 38-16. The following game, Hargrave made his first career start and recorded his first career tackle in a 24-16 victory over the Cincinnati Bengals. On November 20, 2016, Hargrave scored his first career NFL touchdown after Ryan Shazier stripped Cleveland. Browns’ quarterback Josh McCown. During the Steelers’ victory he recorded his first career sack on McCown and also finished with a tackle. The next game, Hargrave earned a season-high five combined tackles in the Steelers’ 28-7 victory over the Indianapolis Colts. On December 4, 2016, he suffered a concussion during a victory over the New York Giants and was inactive the following game against the Buffalo Bills. He finished the 2016 season with 27 combined tackle (18 solo), two sacks, and one touchdown in 13 starts and 15 games.

The Pittsburgh Steelers received a playoff berth after finishing atop the AFC North with an 11-5 record. On January 8, 2017, Hargrave started his first career playoff game and recorded one tackle, as the Steelers routed the Miami Dolphins 30-12 in the AFC Wildcard game. After defeating the Kansas City Chiefs in the divisional round, the Steelers went on to face the New England Patriots in the AFC Championship. Hargrave made five combined tackles as the Steelers lost 17-36 to the eventual Super Bowl LI Champions.

Hargrave returned as the starting nose tackle to start the 2017 season after winning the job over Daniel McCullers and Roy Philon. He started the Pittsburgh Steelers’ season-opener against the Cleveland Browns and made three solo tackles and sacked DeShone Kizer in the Steelers’ 21-18 victory. On October 8, 2017, Hargrave recorded a career-high ten combined tackles in a 30-9 loss to the Jacksonville Jaguars.

In week 11 against the Jacksonville Jaguars, Hargrave recorded 4 tackles, 2 sacks, and 1 pass defended as the Steelers won 20-16. Hargrave finished the season with 41 tackles, 6 sacks, and 1 pass defended. He received an overall grade of 82.7 from Pro Football Focus in 2018, which ranked as the 19th highest grade among all qualifying interior defenders.

On March 21, 2020, Hargrave signed a three-year $39 million contract with the Philadelphia Eagles.