[5] On the hardwood, Tate was a teammate of Caris LeVert and made the game-winning tip-in in a playoff win over Columbus Marion-Franklin as a freshman.

Despite standing 6'4", Tate sometimes played center on a Buckeyes team that featured 6'5" point guard D'Angelo Russell.

[10][11] As a junior, Tate led the Buckeyes in scoring with 14.3 points per game, taking the primary role on offense due to an injury to Keita Bates-Diop.

Toward the end of his junior season, Tate contemplated giving up basketball and walking on to Ohio State's football team.

[5] As a senior, Tate was a captain alongside a healthy Bates-Diop, and had some impressive moments including setting an Ohio State record going 10-for-10 from the field in a win over Northeastern in November 2017.

[20] Tate made his NBA debut on December 26, playing 37 minutes against the Portland Trail Blazers; he recorded 13 points, four rebounds, and two assists in the overtime loss.

[22] Tate was selected to the NBA All-Rookie First Team at the end of the season, becoming only the second undrafted player to claim such honors.

[22][23] On December 1, 2021, Tate scored an NBA career-high 32 points while also adding 10 rebounds, 7 assists, 5 blocks, and 2 steals in a win over the Oklahoma City Thunder, becoming only the second Houston Rockets player after Hakeem Olajuwon to achieve these totals in a single game.

[23][25] On January 15, 2023, the NBA suspended Tate for one game without pay for leaving the bench area during an altercation between the Rockets and the Sacramento Kings two days earlier.

During his rookie season with the Houston Rockets, Tate gained a reputation as a strong defender, with his play often compared to PJ Tucker.