[7] Curran was announced as the replacement for Mitchell Starc by Kolkata Knight Riders for the 2018 Indian Premier League,[8] where he played 5 matches and took 6 wickets.

On 25 July 2019, in the 2019 t20 Blast match against Glamorgan, Curran took a hat-trick,[9] finishing with figures of three wickets for three runs from the two overs he bowled.

[14] In December 2023, while playing for the Sydney Sixers, Curran was suspended for 4 matches of the Big Bash season after being found guilty of intimidating an umpire in a pre-match altercation.

[16] He received his first call-up to a full English squad in February 2017, for the One Day International (ODI) tour of the West Indies, as cover for Jake Ball.

[21] In November 2017, Curran was added to England's Test squad as a replacement for Steven Finn for the Ashes series in Australia.

He was the third England bowler in four years, after Ben Stokes and Mark Wood, to miss out on a maiden Test wicket because of a no-ball.

[34] The following month, he was added to England's main squad for the World Cup,[35] replacing his brother, Sam, who was ruled out due to a back injury.