Previously, Burke had been a member of the club's senior academy.
Burke broke into the Glasgow Warriors team squad towards the end of the 2025/26 campaign, making his debut against Fidelity SecureDrive Lions in Johannesburg before earning his first start away to the DHL Stormers in Cape Town the following week.
The lock has also impressed on the international stage, representing Scotland U20 at both the 2024 U20 Six Nations and the 2024 World Rugby U20 Championship.
The 21-year-old continued his development throughout the 2024/25 campaign with Glasgow Warriors A, producing a series of standout performances, including crossing the whitewash in a victory over Benetton U23.