Maye played college football at the University of Florida. He redshirted in 2012. As a freshman in 2013, he played in 8 games, making 16 tackles and an interception. As a sophomore in 2014, he played 11 games with 62 tackles, 5 passes defended, 2 forced fumbles, and an interception. As a junior in 2015, Maye played 12 games with 77 tackles, 4 passes defended, 2 forced fumbles, and 2 interceptions. As a senior in 2016, he played 9 games with 50 tackles, a sack, and an interception.
Collegiate statistics
Professional career
Maye received an invitation to the NFL Combine, but opted to not perform drills and wait until his pro day. At Florida's Pro Day, he chose to perform all of the combine drills except the bench press and completed positional drills for team representatives and scouts. NFL draft experts and analysts projected him to be a second round draft pick. He was ranked as the fourth best free safety in the draft by NFLDraftScout.com, was ranked the seventh best safety by ESPN, and the eighth best safety by Sports Illustrated. The New York Jets selected Maye in the second round of the 2017 NFL Draft. He was the second safety selected by the Jets after they selected LSU'sJamal Adams sixth overall.
2017
On May 23, 2017, the New York Jets signed Maye to a four-year, $6.55 million contract with $3.66 million guaranteed and a signing bonus of $2.90 million. He entered training camp competing against Jamal Adams and Calvin Pryor to be one of the starting safeties. Head coachTodd Bowles named Maye the starting free safety to begin the regular season, alongside strong safety Jamal Adams. He made his professional regular season debut and first career start in the New York Jets' season-opener at the Buffalo Bills and recorded seven combined tackles during a 21–12 loss. In Week 5, Maye recorded four combined tackles, deflected a pass, and made his first career interception off a pass by quarterback Kevin Hogan in the Jets' 17–14 victory at the Cleveland Browns. On October 22, 2017, he collected a season-high seven combined tackles, broke up a pass, and intercepted a pass attempt by Jay Cutler in the Jets' 31–28 loss at the Miami Dolphins. In Week 15, Maye made a season-high tying seven combined tackles during a 31–19 loss at the New Orleans Saints. Maye finished his rookie season in with 79 combined tackles, two pass deflections, and two interceptions in 16 starts.
2018
Maye missed the first three games of 2018 due to a foot injury, but returned in Week 4 as the Jets starting free safety. During Week 5 against the Denver Broncos, Maye intercepted Case Keenum and returned it 104 yards but was a yard shy of scoring a touchdown. Time expired anyhow and the Jets won 34-16. The interception set the NFL record for longest interception return without scoring a touchdown. He then suffered a broken thumb the following week against the Indianapolis Colts and missed the next game. He returned in Week 8, playing in the next three games before suffering a shoulder injury in Week 10 against the Buffalo Bills. He was placed on injured reserve on December 1, 2018, ending an injury-plagued season for Maye.
2019
Maye changed his number from 26 to 20 to accommodate the signing of Le'Veon Bell. In week 16 against the Pittsburgh Steelers, Maye recorded an interception off a pass thrown by Devlin Hodges late in the fourth quarter to seal a 16–10 Jets' win. This was Maye's first interception of the season.
