Nesterov was selected by the Tampa Bay Lightning in the fifth round, 148th overall, of the 2011 NHL Entry Draft. He was also drafted by the Kontinental Hockey League 's Traktor Chelyabinsk, who selected him in the first round, 22nd overall, of the 2010 KHL Junior Draft. He opted to then play two seasons with Chelyabinsk in the KHL. On April 30, 2013, Nesterov was signed to a three-year, entry-level contract by the NHL's Lightning.
Professional
On December 31, 2014, the Tampa Bay recalled Nesterov from the Syracuse Crunch, the team's American Hockey League affiliate. He had played in 32 games with the Crunch during the 2014–15 season, recording three goals and 14 points with a +4 plus-minus rating and 26 penalty minutes. Prior to his call-up, Nesterov has played in 86 career AHL games, all with the Crunch over the past two seasons. He has seven goals and 30 points with 65 penalty minutes. On December 31, 2014, the same day of his call-up, Nesterov made his NHL debut in a 5–1 Lightning victory over the Buffalo Sabres. He was a +1 and logged just over 15 minutes of ice time during the game. On April 16, 2015, Nesterov played in his first career NHL playoff game recording his first playoff goal and point. On April 18, 2015, Nestrov recorded his first NHL playoff assist in a Tampa Bay Lightning 5-1 win over the Detroit Red Wings. On October 16, 2015, the National Hockey League announced that it was suspending Nesterov for two games without pay for boarding Dallas Stars forward Curtis McKenzie. Nesterov was given a five-minute penalty and a game misconduct for checking McKenzie from behind for the incident that led to his suspension. As a result of the suspension, Nesterov forfeited $7,983.88 in pay. On September 26, 2016, the Lightning announced the re-signing of Nesterov to a one-year contract worth $725,000. Nesterov appeared in 57 games this past season, recording three goals and nine points. He set career highs for games played, goals, assists, and points. He also appeared in nine 2016 Stanley Cup Playoff games, recording one assist and nine penalty minutes. Nesterov has appeared in 84 career NHL games over two seasons with the Lightning, recording five goals and 16 points. Nesterov has also appeared in 26 playoff games, recording a goal and seven points. On January 26, 2017, the Lightning traded Nesterov to the Montreal Canadiens in exchange for Jonathan Racine and a 6th round pick in the 2017 NHL Entry Draft. Rumors were started about Nesterov's return to the KHL began when Traktor Chelyabinsk placed his name on the roster on their website, his former team, which is based in Nesterov's hometown. On July 6, 2017, Nesterov's agent posted a tweet stating that Nesterov had decided that he was going to return to Russia to play in the KHL. The following day it was announced that Nesterov agreed to a three-year contract with a KHL powerhouse club, CSKA Moscow.
