Gorshkov made his debut in the Russian Professional Football League for Chertanovo Moscow on 18 August 2016 in a game against Energomash Belgorod.

[1] He made his Russian Football National League debut for Chertanovo on 17 July 2018 in a game against Rotor Volgograd.

Gorshkov made his Russian Premier League debut for Krylia Sovetov Samara on 25 July 2021 in a game against Akhmat Grozny.

[2] On 24 June 2024, Gorshkov signed a contract with Zenit Saint Petersburg for three seasons, with an optional fourth.

[3] Gorshkov was called up to the Russia national football team for the first time in October 2023 for friendlies.