Tate is the oldest son of Jermaine Tate, who played basketball at Ohio State in 1996–97 before transferring to Cincinnati and played professionally overseas. His mother, Cori Key, was stabbed to death by her boyfriend Damiene Boles on July 31, 2004. Boles was convicted of the murder three years later. After his mother's death, Tate was raised by his father and stepmom Jenice alongside their three children. Tate went through anger management to process his emotions and has a tattoo of a key on his leg. Tate attended Pickerington High School Central, where he excelled at basketball and football. He played defensive end and tight end before a shoulder injury cut his junior season short, and he focused on basketball from then on. 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. As a sophomore, his team went 26–2 and won the 2012 Division I championship defeating Toledo Witmer in the final game. Both junior and senior year Tate went on to be a first team conference player and senior year was co-player of the year in the OCC. He injured his shoulder as a junior, shortening his season, but still averaged 22.3 points, 12 rebounds and three assists per game. Tate ended his high school career as the number 1 ranked player in Ohio and the 15th ranked forward in the nation in the ESPN top 100.
College career
As a freshman, Tate posted 8.8 points and 5 rebounds per game. His averages climbed to 12.1 points and 5.5 rebounds per game since becoming a full-time starter against Northwestern on January 22, 2015. Tate was a Big Ten All-Freshman Team selection. Despite standing 6'4, Tate sometimes played center on a Buckeyes team that feature D'Angelo Russell. Tate averaged 11.7 points, 6.4 rebounds, and 1.5 assists per game as a sophomore. He missed the final seven games with a shoulder injury. He was a Big Ten Honorable Mention selection. Tate was an Honorable Mention All-Big Ten selection as a junior. 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. He described a locker room situation in which players had completely given up on the team and did not even want to play in the NIT. A conversation with coach Thad Matta and assistant coach Greg Paulus persuaded Tate to return to the floor for his senior year. He had second thoughts after Matta was fired in favor of Chris Holtmann, but Holtmann and Tate developed a strong relationship. 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. Tate scored 14 points going 6-for-11 from the field in a comeback victory over Michigan in December. He averaged 12.3 points and 6.2 rebounds per game as a senior on a NCAA Tournament squad that finished 25-9. He was named to the Second Team All-Big Ten by the coaches and honorable mention all-conference by the media. Tate finished as Ohio State’s 19th-leading scorer with 1,512 points. After the season, he worked with coach Joey Burton to improve his shooting technique in preparation for a professional career.
Professional career
After going undrafted in the 2018 NBA draft, Tate joined the Milwaukee Bucks for the 2018 NBA Summer League. However, he was unable to play for the Bucks due to a fractured finger on his right hand. On August 20, 2018, he signed in Belgium with the Antwerp Giants. In 42 league games, he averaged 10.2 points, 3.9 rebounds and 1.7 assists per game. He also averaged 13.0 points, 5.6 rebounds and 1.6 assists in 24 BCL games. On July 22, 2019, Tate signed with the Sydney Kings in Australia for the 2019–20 NBL season He averaged 16.4 points, 2 assists, and 5.8 rebounds per game and was named to the All-NBL First Team.