After playing youth football for AVV Zeeburgia, Van der Kust joined FC Utrecht's academy in 2012.[3] He signed his first professional contract with Utrecht in December 2019, with the deal valid until mid-2022 with the option of a year's extension.[3] Van der Kust made his debut for Jong Utrecht on 10 January 2020 in a 2–1 defeat to De Graafschap.[2] He ended the season with 2 appearances for Jong Utrecht, playing primarily with the U-19 side.[2] He scored his first career goal on 24 November 2020 in a 1–1 draw with Jong PSV. During the 2020–21 season he established himself as a regular for Jong Utrecht, making 26 appearances and scoring 1 goal.[4]
On 15 August 2021, he made his Eredivisie debut for Utrecht in matchweek 1 of the 2021–22 season, coming on as a substitute in a 4–0 win over Sparta Rotterdam.[5] On 9 November van der Kust signed a new contract lasting until 2025.[6] He made his first start for Utrecht on 5 February 2022 in a 3–2 win over SC Cambuur.[7][8] Van der Kust started 11 of Utrechts final 14 Eredivisie matches, helping them to a 7th place finish.[8][9] He also started both of Utrecht's European playoff matches, a 4–3 aggregate loss to Vitesse.[8] He made 17 appearances and scored 1 goal for Jong Utrecht during the season.[8]
Van der Kust started the 2022–23 season as the first choice leftback, appearing in 8 of the first 10 Eredivisie games with 7 starts and starting a KNVB Cup game.[10] He then lost his spot in the first team, appearing in just 1 of the next 12 matches, his 1 appearance being a substitute in a cup match, and playing in 3 matches for Jong Utrecht.[10]