Born in Kingston upon Thames, London, Gilchrist started his career at local side Old Isleworthians Youth F.C.

[11][12] He was included in Chelsea's pre-season tour squad in preparation for the 2023–24 season,[13][14] and came on as a substitute at half-time in a 5–0 win against Wrexham.

[16] On 27 December, Gilchrist made his senior debut, subbed-on in stoppage time, in a 2–1 win against Crystal Palace in the Premier League.

[17] Gilchrist's first start for the senior squad came on 6 January 2024, in Chelsea's 4–0 defeat of Preston North End in the FA Cup.

[19] On 15 April 2024, after coming on as an 88th minute substitute for Malo Gusto, Gilchrist scored his first goal for Chelsea in a 6–0 win over Everton.