In June 2019, he captained the Dublin District Schoolboys League representative team to winning the prestigious Kennedy Cup.
[5] His debut came on 17 October 2020 in a 3–1 win over Athlone Town at age 14, making him the youngest player in League of Ireland history.
[7] On 25 July 2021, it was announced that Curtis, as well as his brother Ben, had signed for St Patrick's Athletic, where they would initially play with the club's under 19 side.
[16] His first appearances in European competition came in the summer of 2022 when he came off the bench in a 1–1 draw with NŠ Mura of Slovenia[17] and in a 1–0 away win against Bulgarian side CSKA Sofia in the UEFA Europa Conference League.
[27] On 19 May 2023, Curtis scored the first goal of his senior career, heading home a Jake Mulraney corner in a 1–0 Dublin derby win away to Shelbourne at Tolka Park.
[29] On 30 June 2023, Curtis scored a header from a Jake Mulraney corner to give his side a 3-goal lead in an eventual 7–0 win over UCD at Richmond Park.
[35][36] On 25 January 2024, Curtis signed for Premier League club Sheffield United for an undisclosed international training compensation fee, on a contract until 2027.
[41] On 2 August 2024, Curtis joined EFL League One side Peterborough United on a season long loan deal.
[44] On 17 January 2025, Curtis was loaned to St Johnstone until the end of the season, with the side bottom of the Scottish Premiership at the time of joining.