Alexander (6-1, 227) spent the past four seasons (2015-18) with the Tampa Bay Buccaneers after the team selected him in the fourth round (124th overall) of the 2015 NFL Draft. With the Buccaneers, he started in all 46 games in which he appeared and registered 380 tackles, 22 passes defensed, 7.0 sacks, six interceptions (one returned for a touchdown), six forced fumbles and two fumble recoveries. Since 2015, he is one of four players in the NFL to register at least 300 tackles, 6.0 sacks and six interceptions (Thomas Davis, Luke Kuechly and Harrison Smith).

As a rookie in 2015, Alexander earned PFWA All-Rookie honors after registering 93 tackles, nine passes defensed, 3.0 sacks, two interceptions, two forced fumbles and one fumble recovery. In 2016, he registered 145 tackles, including an NFL-high 108 solo tackles, according to gamebook statistics, while adding 3.0 sacks, one interception, seven passes defensed, one forced fumble and one fumble recovery. The following season, Alexander earned Pro Bowl honors after notching 97 tackles, four passes defensed, three interceptions and one forced fumble. In 2018, he started all six games in which he appeared and finished with 45 tackles, two passes defensed, two forced fumbles and 1.0 sack.