Zeegers played youth football for Slekker Boys, Fortuna Sittard and PSV, eventually signing his first professional contract with the latter in 2019; a two-year deal.[3][4]
He joined MVV on a six-month loan on 12 January 2021.[7] He made his debut for the club on 15 January 2021, starting at right-back in a 3–0 away loss to Go Ahead Eagles.[8] He provided his first assist on 12 April, a cutback pass to Jérôme Déom who slotted home for the 1–0 lead in an eventual 4–2 home loss to rivals Roda JC Kerkrade.[9][10]
On 4 June 2021, the deal was made permanent and Zeegers signed a two-year contract with MVV.[11] He suffered a foot injury during practice in November 2022, which required surgery. The injury ruled him out for several months.[12]