On June 21, 2018, Carter was selected by the Memphis Grizzlies in the second round of the 2018 NBA draft with the 32nd overall pick. On July 12, 2018, the Memphis Grizzlies announced that they had officially signed with Carter. During his rookie season, he has had multiple assignments to the Memphis Hustle, the Grizzlies' G League affiliate. Carter made his NBA debut on December 15, 2018, coming off the bench in a 97–105 loss to the Houston Rockets with eleven points, two steals, a rebound and a block. On April 10, 2019, Carter scored a then-career-high 32 points along with four rebounds, two assists and a steal in a 132–117 win over the Golden State Warriors.

Jevon converted to the point guard position at West Virginia, making his name as one of the top defensive players in the Big 12 Conference. He was one of the architects of "Press Virginia", coach Bob Huggins's defensive scheme that forces many turnovers. Carter became a starter as a sophomore and averaged 9.5 points and 2.3 rebounds per game.