2008-09: Nikita Nesterov played in the Traktor Chelyabinsk youth program.
2009-10: Nesterov played for the Traktor Chelyabinsk club and made his debut with Belie Medvedi Chelyabinsk in the MHL (Russian U22 league) as a 16-year-old. He scored 5 goals with 2 assists and had 14 penalty minutes in 13 games (including playoffs). Nesterov skated in all seven games for fourth-place Russia at the 2010 U18 World Junior Championship and scored 2 goals with 29 penalty minutes. Nesterov was selected by Traktor Chelyabinsk in the first round (22nd overall) of the 2010 KHL Draft and was selected by the Tri-City Americans (WHL) in the first round (16th overall) of the CHL Import Draft.
2010-11: Nesterov skated in 46 games for Belie Medvedi Chelyabinsk in the MHL. He scored 5 goals with 14 assists and had 72 penalty minutes. He played for Russia in both the
2010 U19 World Junior A Challenge and 2011 U18 World Junior Championship. Nesterov had 1 goal with 6 penalty minutes in four U19 games and scored 2 goals with 2 assists and was plus-11 with 29 penalty minutes in seven games for the bronze-medal winning U18 squad. He was ranked 32nd amongst European skaters in Central Scouting's final rankings and was selected in the fifth round (148th overall) by Tampa Bay in the 2011 NHL Draft.
2011-12: Nesterov skated in 10 KHL games for Traktor Chelyabinsk and was the third-leading scorer among MHL defensemen playing for Chelyabinsk's junior team, Belie Medvedi. He represented Russia at the 2012 U20 World Junior Championship. Nesterov had 1 assist and was plus-eight with 4 penalty minutes during the regular season with Traktor. He saw limited ice time in three playoff games – with no points or penalty minutes. He had 11 goals with 20 assists in 41 MHL games, finishing just three points off the league-high despite playing a dozen fewer games. In seven games at the WJC he scored 2 goals with 3 assists and was plus-seven with 6 penalty minutes as Russia defeated the d Finland to win the bronze medal.
2012-13: Nesterov played in 35 KHL games as a 19-year-old and played for the club's MHL junior team, Belle Medvedi. He was an assistant captain for Russia at the 2013 World Junior Championship in Ufa. He was +6 with no points and 14 penalty minutes skating for Traktor Chelyabinsk. Traktor finished second in the Kharlamov Division and reached the KHL Finals against Dynamo Moscow. Nesterov had 4 assists and was -3 with 6 penalty minutes in 19 playoff games. He played six games with Belle Medvedi, including four playoff games, and scored 2 goals with 2 assists; finishing -4 with 2 penalty minutes. In seven games at the WJC he had 4 assists and was +1 with 2 penalty minutes. Russia defeated Canada in overtime in the bronze medal game. Nesterov signed a three-year, entry-level contract with Tampa Bay in April of 2013.