After coming up through the ranks with his native Gomel and later
HC Dinamo Minsk Korobov was signed to a two-year entry-level deal with the
Tampa Bay Lightning on 2 August 2012. In the final year of his contract with the Lightning, Korobov was recalled from
American Hockey League affiliate, the
Syracuse Crunch, and made his NHL debut, featuring in 3 games in the
2013–14 season. On 1 July 2014, Korobov opted to return to the KHL as a free agent, signing a two-year contract with
Atlant Moscow Oblast. After playing a further two seasons with Dinamo Minsk, Korobov left the club for the third time in his career, agreeing to a two-year deal with Russian club,
Torpedo Nizhny Novgorod beginning from the
2018–19 season, on July 14, 2018. Korobov left Torpedo after just one season, opting to continue his career in the KHL with Amur Khabarovsk for the
2019–20 season on 4 August 2019. Korobov played in 29 regular season games with Amur, collecting just 2 goals, before he was hampered by injury. As a free agent, Korobov continued his tenure in the KHL, agreeing to a one-year contract with Salavat Yulaev Ufa on 2 May 2020. ==International play==