Born in Greystones, Power started his career as a youth player for Greystones United and later played youth football for St Josephs Boys, Cabinteely before making his senior debut for Cabinteely in August 2015 as a substitute against Finn Harps. He later signed for UCD, where he made 13 league appearances and scored one goal.
In January 2018, Power joined Norwich City on an 18-month contract following a trial period with the club. Power agreed a two-year extension to his deal in January 2019, six months before it was due to expire, and also joined Eerste Divisie side Dordrecht on loan until the end of the season. He made 10 appearances for Dordrecht and scored one goal.
On 4 July 2019, Power joined newly promoted Scottish Premiership side Ross County on loan. On 13 July 2019 he made his debut for the club against Montrose in the Scottish League Cup. However, he was recalled by Norwich in January 2020 after making just 4 senior appearances. Later that month, he joined National League North side Kings Lynn Town on loan until the end of the season. He made six appearances and scored twice as Kings Lynn were promoted to the National League.
In August 2020, he returned to Kings Lynn Town on a season-long loan. His loan was cut short in January 2021 in order to join Harrogate Town on a permanent deal, having made 13 appearances and scored two goals in all competitions.