Described as a tall left-arm quick capable of extracting significant bounce,[2] Haskett featured for Claremont-Nedlands in grade cricket and took 21 wickets at an average of 19.62 during the 2022–23 season, leading to a call up to the Western Australia second-XI. He was awarded a rookie contract with Western Australia in May 2023.[3]
Haskett was brought into the Western Australia match day squad for their opening fixture of the 2023–24 Sheffield Shield season, at home against Victoria.[4] He subsequently made his first-class debut in the match starting on 3 October 2023.[5] His maiden wicket in first class cricket was Travis Dean in the Victorian first innings.[6]
In December 2023, Haskett signed with the Perth Scorchers ahead of the 2023–24 Big Bash League season.[7] In April 2024, he was upgraded from a rookie contract to a full contract with Western Australia.[8]