Clarke's father Joshua was a craftsman from Leeds who set up a church decorating and stained glass studio in Dublin in 1886. Harry was trained in stained glass by Harry Nagle at his father's studio, and by A. E. Child at the Dublin Metropolitan School of Art. In 1913, having completed his education, he moved to London, rented a studio and set himself up as a book illustrator. Picked up by London publisher Harrap, he started with two commissions which were never completed: Samuel Taylor Coleridge's The Rime of the Ancient Mariner (his work on which was destroyed during the 1916 Easter Rising) and Alexander Pope's The Rape of the Lock.