His first play Alaska was produced upstairs at the Royal Court in 2007, and he won the inaugural Tom Erhardt Award for promising new playwright in 2008.

[6] Commissioned by Royal & Derngate, Moore's play Town is a contemporary story inspired by local 19th-century poet John Clare's struggle with madness and his walk from London to Northampton.

[7] His play The Swan premiered as part of a double feature in a production staged in the National Theatre's Paintframe, where the sets are usually painted, in 2011.

He has also written for television, creating the 2015 comedy-drama series Not Safe for Work and contributing episodes of Killing Eve and Temple.

Moore created the historical drama Mary & George, based on Benjamin Woolley's non-fiction book The King's Assassin.