[2][3] On 16 November 2015, Tarasov made his Junior Hockey League (MHL) debut with Tolpar Ufa in a 6–4 win against the Chaika Nizhny Novgorod.

[5] He returned for the next season for Tolpar Ufa, earning the starting goaltending position with 40 games played and a 1.85 GAA and .928 SV%.

[7] On 10 September 2018, Tarasov made his professional debut for the Toros Neftekamsk of the Supreme Hockey League (VHL) in a 6–1 win against the KRS-BSU.

[13] Because of the COVID-19 pandemic, he split his time between Salavat Yulaev in the KHL and the Blue Jackets' AHL affiliate, the Cleveland Monsters.

[18] After both Blue Jackets goaltenders were out with an illness, on 2 December 2021, Tarasov made his NHL debut on an emergency call-up with 34 saves in a 3–2 loss against the Dallas Stars.

[19][20] Tarasov earned his first-career NHL win on October 23, 2022 in Madison Square Garden when the Blue Jackets defeated the New York Rangers 5–1.

[22] Throughout the 2022–23 season, Tarasov has been splitting time between the Cleveland Monsters and Columbus Blue Jackets, backing up goalies Elvis Merzļikins and Joonas Korpisalo while they dealt with injury.