Käit joined the Levadia youth academy in 2006, when Levadia and Kotkas Juunior merged. In July 2014, he joined Fulham academy.[2] Käit signed his first professional contract with the club in July 2015.[3] On 1 March 2017, he signed a contract extension which would keep him at Fulham until the summer of 2019.[4]
Ross County (loan)
On 31 January 2018, Käit joined Scottish Premiership club Ross County on loan until the end of the season.[5][6] He made his debut for the club on 3 February 2018, in a 4–1 away win over Dundee.[7]
Domžale
On 16 June 2019, Käit signed a three-year contract with Slovenian PrvaLiga side Domžale.[8] He made his debut for the club on 11 July 2019, in a 4–3 away win against Balzan in the first qualifying round of the UEFA Europa League.[9] Käit left the club on 3 September 2021.[10]
Bodø/Glimt
On 16 September 2021, Käit signed a contract with Norwegian champions Bodø/Glimt until the end of the year.[11]
Rapid București
On 18 January 2022, Käit signed a two-and-a-half-year contract with Romanian club Rapid București until the summer of 2024.[12]
He made his senior international debut for Estonia on 6 January 2016, in a 1–1 draw against Sweden in a friendly.[13] Käit scored his first two international goals for Estonia on 7 October 2016, in a 4–0 home victory over Gibraltar in a qualification match for the 2018 FIFA World Cup.[14] On 3 September 2017, Käit scored the only goal of a home win over Cyprus in injury time.[15] The goal later earned him the Estonian Silverball award for the best goal scored for the national team in 2017.[16] He scored again in the successive qualifier on 7 October, a 6–0 away win over Gibraltar.[17] Käit was Estonia's highest goalscorer in the qualification with four goals.
^Kangur, Kristjan Jaak (3 September 2021). "Käit ja Domžale lõpetasid lepingu". Soccernet.ee - Jalgpall luubi all! (in Estonian). Retrieved 3 September 2021.