He played college football at LSU, where he was a two-time consensus All-American selection and winner of the Jim Thorpe Award as a junior in 2019.

On August 25, 2020, it was announced that Delpit was officially placed on injured reserve after it was confirmed he had torn his Achilles tendon the previous day and would have to undergo surgery while missing his entire rookie season.

[11][12] During training camp, Delpit competed against Ronnie Harrison to be the starting strong safety after Karl Joseph became a free agent.

[13] Head coach Kevin Stefanski named Delpit the primary backup safety behind starters John Johnson and Ronnie Harrison.

[14] On September 19, 2021, Delpit made his long-awaited professional regular season debut and recorded six combined tackles (three solo), forced a fumble, and earned his first career sack in a 21–31 win against the Houston Texans in the home-opener.

[17] He completed the 2021 NFL season with a total of 66 combined tackles (43 solo), three pass deflections, one sack, a forced fumble, and an interception in 15 games and seven starts.

[26] In Week 9, he racked up a season-high ten combined tackles (eight solo) and was credited with half a sack as the Browns routed the Arizona Cardinals 27–0.

[9] The Cleveland Browns played the Jacksonville Jaguars the same day and Delpit recorded six combined tackles (five solo) and one sack before exiting the 31–27 victory due to an injury he sustained while blitzing Trevor Lawrence.

[27] He finished the 2023 NFL season with a total of 80 combined tackles (63 solo), four pass deflections, one interception, and a fumble recovery in 13 games and 13 starts.

In Week 5, Delpit had seven combined tackles (five solo) in the Browns' 13–34 loss at the Washington Commanders, before exiting in the fourth quarter due to an injury.

Rye following week, he made six combined tackles (five solo) before leaving in the fourth quarter of a 32–41 loss at the Denver Broncos due to a concussion.