Following a stint with the Florida Gators, he played college football for the NC State Wolfpack and was selected by the Patriots in the third round of the 2016 NFL draft.

He spent his next three seasons alternating as the starter and backup with the Miami Dolphins, Cleveland Browns, and Washington Commanders, before rejoining the Patriots in 2024.

Brissett started his second game of the season on November 17 against Jacksonville State after Driskel was unable to play due to injury.

After a 13–13 tie in regulation, Brissett threw an interception to Tyrann Mathieu in the first play of overtime, leading to an Arizona Cardinals 16–13 victory.

[48] During a Week 5 matchup against the San Francisco 49ers, Brissett completed 22-of-34 pass attempts for a career-high 314-yards and an interception, as the Colts won 26–23.

[50] After a six-game losing streak, Brissett had 114 passing yards and a touchdown in the regular season finale victory over the Texans.

[54] In Week 3 against the Philadelphia Eagles, with the Colts down 20–16 with seconds left in the game, Brissett replaced Luck to attempt a Hail Mary pass from his own 46-yard line.

[55] In a Week 12 win over the Dolphins, Brissett was brought in and completed a 4th and short throw to Luck, who was lined up as a receiver.

Colts general manager Chris Ballard confirmed in a subsequent press conference that Brissett would be the full-time starting quarterback going into the season.

[60] In Week 1 against the Los Angeles Chargers, Brissett threw for 190 yards and two touchdown passes to T. Y. Hilton in a 30–24 overtime loss.

[64] In Week 5, against the eventual Super Bowl champions Kansas City Chiefs, Brissett threw for 151 yards and ran for their lone touchdown in the 19–13 win.

[75] Brissett was named the starter for the Dolphins Week 3 matchup against the Las Vegas Raiders due to Tagovailoa's injury.

[78] Due to Deshaun Watson's sexual misconduct allegations and his 11-game suspension, Brissett was named the Week 1 starter for the game against the Carolina Panthers.

[81] He played for the first time in the 2023 season in Week 15 against the Rams, where he came in relief of Sam Howell, who was benched in the fourth quarter.

[83] When Howell was benched a second time in the following game against the New York Jets, Brissett came in the third quarter down by 20 points, and led 3 straight touchdown drives to take the lead.

[85] On December 27, 2023, head coach Ron Rivera announced that Brissett would be the team's starting quarterback for Week 17 against the 49ers.

[88] On August 29, head coach Jerod Mayo named Brissett the starting quarterback over rookie Drake Maye to begin the season.

[91] In Week 8 against the Jets, Brissett made an appearance in relief of Maye, who exited the game in the second quarter due to a head injury.