Ku sii qor faqradan - Markii ugu horeysay ee uu ka ciyaaro ISU Challenger Series (CS), Kvitelashvili wuxuu kaalinta shanaad ka galay Lombardia Trophy bishii Sebtember 2014. Bishii Nofeembar, wuxuu ku tartamay 2014 Rostelecom Cup, isagoo badalay Kolyada oo dhaawacmay; wuxuu dhammeeyay kaalinta laba iyo tobnaad ee tartanka, waa abaalmarintii ugu horreysay ee abaalmarinta Grand Prix (GP) ee xirfadiisa. Ka dib markii uu kaalinta sideedaad ka galay tartanka horyaalka Ruushka ee 2015
, waxaa loo diray Universiade-kiisii labaad ee Jiilaalka wuxuuna kaalinta toddobaad ka galay tartanka, oo lagu qabtay bishii Febraayo 2015 magaalada Granada, Spain.