Drinan began playing football with his local side Carrigaline United, impressing enough to earn a move to Cobh Ramblers, where he would play with their Under-19 side for a short time in early 2015 before moving to their rivals Cork City in the summer of 2015 where he would play until the end of the 2017 season. During his time at Cork's under-19 side, he played alongside Chiedozie Ogbene, Cian Coleman and Conor McCarthy among others.
Drinan dropped down a division to sign for Waterford of the League of Ireland First Division in July 2017, making his competitive debut in senior football away to Cabinteely on 4 August 2017. He scored the first goal of his senior career on 1 September 2017, scoring in a 1–1 draw with Shelbourne at the RSC. Drinan finished up the season with 5 appearances and 1 goal to his name as Waterford won the League of Ireland First Division, resulting in his first taste of silverware at senior level.
Drinan began training with EFL Championship side Ipswich Town in October 2017 and was announced as a new signing by manager Mick McCarthy on 4 January 2018. He was an unused substitute in 4 EFL Championship games and 1 FA Cup game for Ipswich but failed to make his first team debut as his side finished in 12th place. He joined National League side Sutton United on 1 August 2018. His first goal came on 20 October 2018 when he scored the winner against Wealdstone in the FA Cup. On 15 February 2019, it as announced that Drinan had signed for his old club Waterford on loan until the summer. His loan was a huge success, scoring 7 goals in 18 league games. His form had Waterford looking to extend the loan, but this proved to be unsuccessful, with Ipswich wanting the player to return. Drinan signed for Swedish Superettan side GAIS on 8 August 2019. He made his debut away to Dalkurd FF on 18 August 2019. He returned to Ipswich Town in November at the end of his loan which saw him make 9 appearances for GAIS. He signed for Scottish Championship side Ayr United on loan on 17 January 2020. His debut came the next day in a 1–0 Scottish Cup win over Ross County to earn a 5th Round tie with Scottish Premiership sideSt Johnstone.
International career
Drinan received his first call up to the Republic of Ireland U21 national team in February 2019 for a training camp at the FAI National Training Centre. He made his debut for the under-21's in a UEFA European Under-21 Championship qualifier on 24 March 2019, featuring as a second-half substitute in a 3–0 victory over Luxembourg in Dublin.
