Thompson played college football for the Boise State Broncos, and was selected by the New York Giants in third round of the 2016 NFL draft.

Thompson was rated as a three-star recruit and committed to Boise State University to play college football.

At the conclusion of the pre-draft process, Thompson was projected to be a second to fourth round pick by NFL draft experts and scouts.

[13] He entered training camp competing with Nat Berhe and Mykkele Thompson for the vacant starting free safety position.

Head coach Ben McAdoo named Thompson the backup free safety to begin the regular season, behind Nat Berhe.

He made a season-high four solo tackles before exiting in the fourth quarter of the Giants' 16–13 win against the New Orleans Saints due to a foot injury.

[16] On November 9, 2016, the Giants placed Thompson on injured reserve after he missed six games (Weeks 3–9) due to his foot injury that required surgery.

On October 8, 2017, Thompson collected a season-high 11 combined tackles (eight solo), two pass deflections, and made his first career interception during a 27–22 loss to the Los Angeles Chargers in Week 5.

Thompson made the interception off a pass by Chargers' quarterback Philip Rivers, that was originally intended for wide receiver Keenan Allen, in the third quarter.

[22] On September 1, 2018, Thompson was waived/injured by the Giants as part of final roster cuts after losing the starting safety job to Curtis Riley.

In week 4, Thompson was replaced after the first drive of the Cleveland Browns, because he failed to defend a 37-yard touchdown trick pass from Jarvis Landry to fellow wide receiver Odell Beckham Jr., opening the door for second-year player Donovan Wilson to take over the full time starting position.

Thompson would return as the starter at strong safety in place of an injured Wilson in Week 13 against the Baltimore Ravens on Tuesday Night Football, recording his first interception as a Cowboy off a pass thrown by Lamar Jackson during the 34–17 loss.