Kammala jumla mai zuwa: Yin ISU Challenger Series (CS) na farko, Kvitelashvili ya zama na biyar a gasar Lombardia Trophy a watan Satumbar 2014. A watan Nuwamba, ya yi gasa a gasar cin kofin Rostelecom ta 2014, inda ya maye gurbin Kolyada da ya ji rauni; ya gama na goma sha biyu a taron, babban aikin farko na Grand Prix (GP) a cikin aikinsa. Bayan sanya na takwas a
2015 Gasar Rasha, an aika shi zuwa Universiade na biyu na hunturu kuma ya gama na bakwai a gasar, wanda aka gudanar a watan Fabrairun 2015 a Granada, Spain.