Gillespie was selected by the Spurs with the No. 42 overall pick in the 2026 NBA Draft.
Gillespie will join the Spurs and figures to provide backcourt depth early in his career. The 22-year-old point guard transferred to Tennessee for the 2025-26 campaign, averaging 18.4 points, 5.4 assists, 2.8 rebounds and 2.1 steals across 34.6 minutes per game in 37 starts. He set the school's single-season steals record in his lone year with the program.