As a junior, Kartsev competed at the 2017 European Youth Olympic Festival where he was part of the Russian team alongside Yuri Busse and Sergei Naidin that won the team gold medal ahead of Great Britain and Switzerland.

[2] Kartsev represented Russia at the 2021 European Artistic Gymnastics Championships in Basel, Switzerland.

He placed third in the all-around during qualifications but did not reach the final due to the two-per-country rule, as his teammates Nikita Nagornyy and David Belyavskiy finished ahead of him.

[4][5] In June 2021, Kartsev was named to the Russian men's gymnastics team for the Tokyo Olympics alongside Nikita Nagornyy, David Belyavskiy and Artur Dalaloyan.

[6] However, it was later announced that Kartsev would compete at the Games as an individual, and Denis Ablyazin would take his place on the team.