Graham joined Aston Villa in 2011. The club had a large Irish contingent at the time that included Dan Devine and Mikey Drennan and he formed a good partnership up front with Mikey in the academy.
Graham finished as top scorer in the 2012-13 edition of the Next-Gen Series, the forerunner of the Under-19 Champions League. He made two first team appearances for Villa, both in the League Cup.
Graham had short loan spells at Shrewsbury Town and Notts County before the Under-21 international signed a permanent deal at Meadow Lane in 2015. Altogether he scored 5 goals in 52 competitive appearances for Notts, including a wonder strike against his former club in a League Cup tie at Villa Park.
Graham scored a goal and was sent off moments later on his Shamrock Rovers debut at Oriel Park on 2017 opening day. He netted a further 9 goals in that campaign, including 3 strikes in the Europa League, before his season was cut short by injury.