Second-row Cockburn joined from Melrose where he played in the Arnold Clark Premiership. He also featured for Scotland in the 2025 World Rugby U20 Championship.
His professional debut came in March 2026, starting at outside centre in a 38-17 win over a Leinster side that boasted British & Irish Lion, Robbie Henshaw, and former All Black, Rieko Ioane, as its centre pairing.