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Rustavi was the club Kvaratskhelia played for after Dinamo Tbilisi. He joined Rustavi in 2017, spending two seasons with the club before moving to Rubin Kazan in 2019. During his time at Rustavi, Kvaratskhelia made a significant impact, helping the team win the Georgian Cup in 2018. He also earned individual recognition, being named the Georgian Footballer of the Year in 2018.