Pedzisa mutsara unotevera: 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. Pashure pokuva wechisere pa
2015 Russian Championships, akatumirwa kuWinter Universiade yake yechipiri uye akapedza wechinomwe pamakwikwi, akaitwa muna Kukadzi 2015 muGranada, Spain.