Kluivert came through the AFC Ajax youth program.[3] He made his Eerste Divisie debut with Jong Ajax on 16 September 2016 in a game against MVV, replacing Vince Gino Dekker in the 67th minute, in a 1–0 away loss.[4] Kluivert made his first team debut in the Eredivisie on 15 January 2017 in a 1–3 away win against PEC Zwolle, when he replaced Amin Younes in the 39th minute.[5] He scored his first Eredivisie goal on 19 March 2017 in an away match against SBV Excelsior, exactly 10 years and 1 day after his father's last career goal. The match ended in a 1–1 draw.[6]