Kunyora kuenderera kweiyi ndima - Kuita yake ISU Challenger Series (CS) kutanga, Kvitelashvili akaisa yechishanu paLombardia Trophy munaGunyana 2014. MunaNovember, akakwikwidza pa2014 Rostelecom Cup, achitsiva Kolyada akakuvara; akapedza gumi nemaviri pachiitiko ichi, yekutanga mukuru Grand Prix (GP) basa rebasa rake. Mushure mokupinda munzvimbo yechisere pa2015 Russian Championships
, akatumirwa kuWinter Universiade yake yechipiri uye akapedza wechinomwe pamakwikwi, akaitwa muna Kukadzi 2015 kuGranada, Spain.