Cosgrave developed his foundational skills within the academy systems of several prominent clubs, spending time in the youth setups at Queens Park Rangers, Colchester United, and Brentford FC. While at Brentford, he notably featured in the FA Youth Cup.

Senior Career

Grays Athletic & Bishop's Stortford (2023–2024): Making his transition to senior football, Cosgrave played 15 times for Grays Athletic, netting 3 goals. He then briefly joined Bishop's Stortford, making his debut in the National League North.

Sittingbourne (2024–2025): Cosgrave enjoyed a highly successful campaign with the "Brickies". He became a focal point in their midfield, making 41 appearances and scoring 4 goals. He was instrumental in Sittingbourne's historic run to the FA Trophy Quarter Finals, which included standout performances and a stunning free-kick goal against Dover Athletic. He also had a brief 5-game loan spell with Cambridge City toward the end of this campaign.

Canvey Island & Cambridge City (2025–2026): In the summer of 2025, Cosgrave initially signed with Isthmian Premier side Canvey Island. By October 2025, he returned to Cambridge City, securing a permanent move to steady their central midfield.