Kazarian began playing chess at age six after being introduced to the game by her grandfather in Georgia, and began competing a year later. She earned the Woman FIDE Master (WFM) title by finishing runner-up in the under-12 girls' division at the European Youth Chess Championships in 2012. Three years later, Kazarian had a career-best performance rating of 2359 at the same tournament in 2015 when she won the under-16 girls' division and earned her first Woman International Master (WIM) norm. She has performed well in national team competitions, earning her two remaining WIM norms in two of her three national appearances, one at the 2015 European Team Chess Championship where she also won an individual bronze medal and the other at the 2016 Chess Olympiad. During the COVID-19 pandemic, she won the first Dutch Women's Internet Chess Championship by defeating Machteld van Foreest in the knockout final.