Kammala jumla mai zuwa: Ya kasance mai tsere a 2012 Eurocup Formula Renault 2.0, kuma zakara a 2012 Formula Renault 2.0 Alps Series da 2013 GP3 Series. Ya fara fitowa a gasar Formula One a matsayin direba na Toro Rosso a matsayin na 15 a Gasar Cin Kofin Duniya. Daga nan sai ya koma Red Bull Racing don yin aiki tare da Daniel Ricciardo don kakar 2015. Ya zira kwallaye na farko na Formula One a gasar Grand Prix ta Hungary ta 2015, inda ya zama na biyu a bayan Sebastian Vettel. A kakar wasa ta farko tare da Red Bull Racing, Kvyat ya gama na 7 a gasar zakarun Turai, a gaban abokin aikinsa. Ya fara kakar 2016 tare da Red Bull Racing, inda ya zira kwallaye na biyu, ya gama na uku a gasar Grand Prix ta kasar Sin ta 2016. Koyaya, bayan haɗarin rikice-rikice a zagaye na farko na tseren gidansa a Sochi, an sauke Kvyat zuwa Toro Rosso kafin Babban Prix na Spain na 2016, inda ya gama kakar kuma ƙungiyar ta riƙe shi a kakar wasa mai zuwa. Kodayake ya nuna kyakkyawan wasan kwaikwayon a cikin shekara ta 2017, lokacinsa ya sha wahala daga matsaloli daban-daban, gami da yin ritaya da yawa a tsere inda zai iya samun maki. Bayan da
2017 United States Grand Prix, Kvyat da Red Bull sun rabu da hanyoyi, suna ƙare kwangilarsa. Kvyat ya shafe shekara ta 2018 a matsayin direban ci gaba na Scuderia Ferrari, kafin Toro Rosso ya sake sanya hannu don kakar. A gasar Grand Prix ta Jamus ta 2019 Kvyat ya yi ikirarin podium na uku a cikin aikinsa ta hanyar kammala na uku; wannan kuma shi ne karo na biyu da Scuderia Toro Rosso ya kammala bayan da suka lashe gasar Grand Prix ta Italiya ta 2008 tare da Sebastian Vettel.