Parr was born in St Helens, Lancashire. His mother is American and he holds dual nationality with both the United Kingdom and the United States because of it. He trained at the Elizabeth Hill School of Dance and Drama in St Helens, and East 15 Acting School in Essex, graduating in 2008. Prior to getting the part in Emmerdale, Parr worked between acting jobs as a Learning Support Assistant in the Special Educational Needs department of a school in Essex. He also worked as a barman.
Previous television appearances include Hollyoaks, Casualty, Good Cop, Inside Men and the BBC daytime soap opera Doctors. Film roles include Queesnbury Rules, No Way Through, and Keiren in the 2011 film Territory. Parr has also appeared on stage in various roles, including Justin in Studies for A Portrait at the Oval House Theatre, Paul in The Back Room at the Cock Tavern, and Danny in Twothousandandsex at the Drill Hall in London.