Tamirlan is a trainee of the capital's hockey. The defenceman played in North American hockey leagues from 2015 to 2020. In the 2019/20 season, Gaitamirov was captain of Kazakhstan's youth national team at the World Championship in the elite division. He has played for teams from the Barys system since 2020. In 2023, Gaitamirov helped Nomad to become the national champion.