His parents are Pille and Risto. Pille was a professional table tennis player. Veesaar grew up in Tallinn, Estonia and was quickly identified as an intriguing young talent because of his height.
He started playing for the Under-16 Estonian national team at age 14 and was playing for the Under-18 team by the time he was 16. He played well in the summer of 2021 as an underage player at the Under-18 European Challenger tournament, averaging 16 points and 11 rebounds. He then got recruited to play with the Real Madrid youth team in 2020 and was solid for Real at the Next Generation Tournament that year and the following season. However, Veesaar was still extremely skinny despite already being 7 feet.
He opted to go to college to develop his frame and chose to attend Arizona to play for Tommy Lloyd, following in Estonian point guard Kerr Kriisa’s footsteps. He was a bench player in his freshman season for the Wildcats, coming off the bench behind Ąžuolas Tubelis. Veesaar missed his entire sophomore season with an elbow injury. During his redshirt sophomore season, Veesaar looked terrific behind Tobe Awaka and Trey Townsend and emerged as a potential NBA prospect again.
However, with Motiejus Krivas returning from an injury, Veesaar transferred to North Carolina for his junior season. He turned into an elite player while entering the starting lineup for the first time. Veesar was named second-team All-ACC. He declared for the 2026 NBA Draft even though he still had one year of college eligibility remaining and stayed in after Michael Malone took over from Hubert Davis as the Tar Heels’ coach.
