Hambardzumyan was a student of the football school
Banants Yerevan, becoming one of the children of the club. Initially he played in the first division for Banants-2. In the 2008 season, he had one match for Banants in the
Armenian Premier League. His debut took place on 23 August in a game against the guest
Ararat Yerevan and ended with a 1–0 defeat of Banants. Hambardzumyan came in on the 84th minute of the match, replacing Seven Muradyan. As of next season, Hambardzumyan was regularly exposed to the participation for matches like the Armenian Premier League and the
Armenian Cup. Banants became the finalists of the Armenian Cup for three seasons in
2008,
2009 and
2010. In the 2010 season, by participating in three events held under the regulation of the
Football Federation of Armenia, Banants came in second in the Premier League, Cup and
Armenian Supercup. On 18 June 2014, Hambardzumyan signed a two-year contract with Macedonian side
FK Vardar. At the end of the 2014–15 season, Hambardzumyan was voted player of the year in Macedonia. In July 2015, Hambardzumyan started both
UEFA Champions League qualification matches against
APOEL FC. In August 2023, he returned to his homeland, signing a contract with
Noah. ==International career==