As a child, he was taken to see a grisly outdoor production of Macbeth on Bodmin Moor, which made a great impression on him.
[2] After leaving Sir James Smith's Comprehensive School in Camelford, he attended University College London to read History and French, before training for an acting career at the Royal Academy of Dramatic Art,[3] where he was in the same year group as Pip Carter, Kathy Rose O'Brien, Arthur Darvill, Sia Berkeley, Harry Hepple, Nathaniel Martello-White, and Danielle Ryan.
[4] His first career move was to join the BBC Radio Drama Company, for which he auditioned when about to leave RADA, winning the Carleton Hobbs Bursary and gaining a contract for five months' work which began a few days after the end of term.
[4] From extensive work in radio, Kloska went on to gain supporting roles in theatre and television and also cameo appearances in films.
In a Royal Shakespeare Company production of Imperium in 2017–2018, Kloska played the slave-narrator Tiro,[5] with one reviewer commenting on his "irrepressible wit and verve".