Dee ihe na-aga n'ihu maka paragraf a - Ọ bụ onye na-agba ọsọ na 2012 Eurocup Formula Renault 2.0, na onye mmeri na 2012 Formula Renault 2.0 Alps Series na 2013 GP3 Series. O mere mbido ya na Formula One dị ka onye ọkwọ ụgbọ ala Toro Rosso na-emecha 15th na World Championship. Mgbe ahụ, ọ kwagara Red Bull Racing ka ọ bụrụ onye otu Daniel Ricciardo maka oge 2015. O nwetara ọkwa mbụ ya na Formula One na 2015 Hungarian Grand Prix, na-emecha nke abụọ n'azụ Sebastian Vettel. N'oge mbụ ya na Red Bull Racing, Kvyat kwụsịrị nke asaa na asọmpi ndị ọkwọ ụgbọala, n'ihu onye otu ya. Ọ malitere oge 2016 na Red Bull Racing, na-agbakọ ọkwa nke abụọ ya, na-agwụ nke atọ na 2016 Chinese Grand Prix. Agbanyeghị, mgbe esemokwu esemokwu n'oge agba nke mbụ nke agbụrụ ụlọ ya na Sochi, Kvyat dara na Toro Rosso tupu 2016 Spanish Grand Prix, ebe ọ kwụsịrị oge ahụ ma ndị otu ahụ jidere ya maka oge ọzọ. Ọ bụ ezie na ọ na-egosipụta arụmọrụ siri ike na 2017, oge ya nwere nsogbu dị iche iche, gụnyere ọtụtụ ezumike nká n'ọsọ ebe ọ nwere ike nweta isi ihe. Mgbe 2017 United States Grand Prix gasịrị
, Kvyat na Red Bull kewara ụzọ, na-akwụsị nkwekọrịta ya n'ụzọ dị irè. Kvyat nọrọ 2018 dị ka onye ọkwọ ụgbọ ala mmepe maka Scuderia Ferrari, tupu Toro Rosso bịanyere aka na ya maka oge a. Na 2019 German Grand Prix Kvyat kwuru ọkwa nke atọ nke ọrụ ya site na imecha nke atọ; nke a bụkwa ọkwa nke abụọ nke Scuderia Toro Rosso mgbe ha meriri 2008 Italian Grand Prix na Sebastian Vettel.