Redmayne made his competitive debut for Central Coast Mariners in September 2008, coming on as an early substitute for the injured Mark Bosnich in a win over Perth Glory. Redmayne made his starting debut for the club one week later in a 3–3 draw with Adelaide United. On 18 January 2010 it was announced he would be joining Brisbane Roar and made his debut for the club as an 80th-minute substitute for regular goalkeeper Michael Theoklitos in a 4–0 win at home to Gold Coast United. He made a second appearance for the Roar in the side's final match of the 2011–12 A-League regular season – again in a win over Gold Coast United. In January 2012, Melbourne Heart announced the Redmayne as their first signing for the 2012–13 A-League season. In January 2013, he made his Heart debut in a victory over Newcastle Jets and was subsequently promoted to first-choice 'keeper at the club. Redmayne returned to New South Wales to play for Western Sydney Wanderers in 2015, where he remained until he moved to Sydney FC in 2017. He subsequently won the A-League Championship with Sydney in 2019 and again in 2020.