Callaghan came to Greater Western Sydney at pick 3 in the 2021 draft out of the Sandringham Dragons and took the club's Rising Star award in 2023. In 2025 the 192cm midfielder averaged 28.4 disposals to sit inside the AFL's top 10, finished runner-up in the Kevin Sheedy Medal and earned a first All-Australian squad selection, adding the Brett Kirk Medal and the club's Goal of the Year. He has played 90 AFL games and kicked 21 goals.