Harper-Penman began his career with local side Barnstaple Town, playing in their youth team. He attended training sessions in Chivenor with the Plymouth Argyle Development Centre before joining the club's Centre of Excellence in 2008 on a two-year contract. Having progressed to the club's youth team, he signed a two-year professional apprenticeship which began in July 2010. He was promoted to the first team squad in April 2011, along with Jake Baker, after impressing manager Peter Reid while playing for the reserve side. "It's all experience for them being with the first team, and you can't buy that," said Reid. He made his debut on 5 April 2011 in a 2–0 defeat at Leyton Orient, replacing Joe Mason as a second-half substitute. Harper-Penman signed his first professional contract in July 2012.