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Club career
In October 2020, he was chosen as one of the 60 of the best young talents in world football among the players born in 2003 by The Guardian.
He made his debut in the Russian Premier League for Dynamo Moscow on 1 November 2020 in a game against FC Tambov.
In the first league game after the winter break of the 2020–21 season, on 28 February 2021 he made his first starting lineup appearance for Dynamo in an away game against FC Akhmat Grozny. In the 7th minute, Zakharyan's cross was stopped by the arm of an Akhmat defender, and Dynamo scored from the penalty kick. In the 37th minute, he scored his first Dynamo goal to make the score 2–0. Dynamo won the game 2–1. He became the third youngest Dynamo player to score a goal in the Russian Premier League, after Aleksandr Kokorin and Pyotr Nemov. In the next game against FC Tambov on 7 March 2021, he assisted on the first Dynamo goal in a 2–0 victory and was selected as player of the match. He was selected as player of the month for February and March 2021 games by Dynamo fans. On 16 May 2021, in the last game of the 2020–21 season, he scored a late winner to establish the final score in a 3–2 victory over PFC CSKA Moscow. He was selected once again as player of the month for May 2021 by fans.
On 27 May 2021 he was voted as player of the season by Dynamo fans. On 15 July 2021, Russian Football Union gave him the Best Under-21 Player award for the 2020–21 season.
On 23 July 2021, he scored Dynamo's first goal on the 2021–22 season, opening the score in a 2–0 away victory over FC Rostov, he was also selected as player of the game.
On 9 December 2021, Russian Premier League awarded him as the league's best under-21 player of 2021.
International career
On 15 March 2021, he was selected for Russia's squad for the 2021 UEFA European Under-21 Championship. He previously represented Russia only up to the Under-17 age bracket and became the youngest player on Russia's squad. In his debut on 25 March 2021 in the opening game against Iceland, he was fouled in the penalty box in the 31st minute, and Russia opened scoring from the penalty kick. In the added time of the first half he scored his first goal to make the score 3–0, with the game eventually ending with a 4–1 victory for Russia. He became the youngest player ever to score a goal for Russia Under-21 squad. He also became the youngest goalscorer in the history of the UEFA European Under-21 Championship, overtaking Yari Verschaeren.
On 11 May 2021, he received his first call-up to the senior Russia squad, he was included in the preliminary extended 30-man squad for UEFA Euro 2020. He suffered a tonsillitis infection in camp and was not included in the final squad.
He made his debut for the senior squad on 1 September 2021 in a World cup qualifier against Croatia. He started the game and was substituted in the second half, as the game ended in a 0–0 draw. He became the youngest outfield player in Russian national team history, playing the game at the age of 18 years, 3 months and 5 days, overtaking Alan Dzagoev. He also became the second youngest national team player overall, behind Igor Akinfeev.