[3] On 22 July 2020, Kastrati signed his first professional contract with Nemzeti Bajnokság I side Újpest after agreeing to a four-year deal and receiving squad number 62.
[5] His debut with Újpest came eight days later against Budafoki MTE after being named in the starting line-up,[6] and assists in his side's only goal during a 1–1 home draw.
On 5 June 2017, Kastrati received a call-up from Kosovo for a 2018 FIFA World Cup qualification match against Turkey.
[13] On 9 October 2017, he made his debut with Kosovo in a 2018 FIFA World Cup qualification match against Iceland after coming on as a substitute at 78th minute in place of Besar Halimi.
[14] On 17 March 2018, Kastrati was named as part of the Kosovo U19 squad for 2018 UEFA European Under-19 Championship elite qualifications.