As a true freshman in 2013, he started 10 of 12 games, recording 38 tackles and three interceptions, and received first-team All-SEC honors at the cornerback position.

As a junior, he made four interceptions, a forced fumble, and four passes defended on 33 tackles in 12 games; he earned All-SEC honors for the third consecutive year.

[22] Throughout training camp, he participated in an open competition for starting cornerback against Brent Grimes, Johnthan Banks, Alterraun Verner, Jude Adjei-Barimah, and Joel Ross.

[24] He made his professional regular season debut and first career start in the Buccaneers' season-opener at the Atlanta Falcons and recorded two combined tackles during a 31–24 victory.

[25] On October 30, Hargreaves collected a season-high eight solo tackles and two pass deflections during a 30–24 overtime loss to the Oakland Raiders in Week 8.

On October 1, 2017, Hargreaves recorded a career-high nine solo tackles and deflected a pass during a 25–23 victory against the New York Giants in Week 4.

[31] On November 12, Hargreaves made three combined tackles before exiting the Buccaneers' 15–10 win against the New York Jets in the third quarter after sustaining a hamstring injury.

[34] In Week 1 against the Saints, Hargreaves recorded seven combined tackles, one pass defensed and forced a fumble that was recovered by teammate Justin Evans and returned for a touchdown.

In Week 2 against the Panthers, Hargreaves made 12 tackles, including a pivotal stop on fourth down; he pushed running back Christian McCaffrey out of bounds short of the first down marker in a 20–14 win.

[43] In Week 9 of the 2020 season against the Jacksonville Jaguars, Hargreaves recorded his first interception as a Texan off a pass thrown by quarterback Jake Luton during the 27–25 win.