 Abeysekera made his professional stage debut with the English Touring Theatre in 2011, playing Valere in "Tartuffe".In 2015, he played Peter Pan on the London stage, and in 2016 he was cast as Puck in the BBC's new production of "A Midsummer Night's Dream".In 2018, Abeysekera began appearing in the Hulu series "Find Me in Paris".