2010-11: Alexander Sharov skated in the CSKA Moscow club program. In nine games with the CSKA junior team he scored 2 goals with 6 assists and had 4 penalty minutes. Sharov played 11 games with the club's 1995-born team and had 5 goals with 3 assists and 4 penalty minutes.
2011-12: Sharov played for CSKA's 1995-born team and played for Kryla Sovetov in the U17 Russian championship. He played for Russia's U17 team at a fall tournament in Vierumaki, Finland and at the Four Nations Tournament in Russia. He scored 13 goals with 21 assists for CSKA. In four games at the Russian championships he scored 3 goals with 2 assists and was -1 with 14 penalty minutes. Sharov played six games with Russia's U17 team and scored 3 goals with 2 assists; finishing -1 with 14 penalty minutes. Sharov was selected by CSKA Moscow in the second round (53rd overall) of the 2012 KHL Draft.
2012-13: Sharov played for Russia in the 2012 Ivan Hlinka Memorial Tournament before making his debut with CSKA Moscow in the MHL U22 league as a 16-year-old. He also represented Russia in the 2012 U19 World Junior A Challenge in Canada. He scored 8 goals with 11 assists and was -7 with 42 penalty minutes in 39 MHL games. Sharov had 2 assists and 2 penalty minutes in four games at the WJAC. In four games for Russia's U18 team at the Ivan Hlinka tournament he had no points and was +3 with 4 penalty minutes.
2013-14: Sharov returned to CSKA Moscow for his second season in the MHL. Sharov was ranked 20th amongst International skaters in Central Scouting's mid-term rankings prior to the 2014 NHL Draft.
A technically sound winger who can also play center, Sharov didn’t progress as expected in the latest couple of seasons. He showed to be a reliable points producer at the junior level, but he’s still inexperienced at the pro level and also didn’t show much in international competition. At this point of his career, Sharov is pretty much a question mark, and in any case needs to improve his consistency, physical play and defensive side of his game before he can be considered anything other than a long shot.