Born in Launceston, Harper attended Launceston Technical High School (now Queechy High School), excelling at athletics. His football was played for City-South in the NTFA, and he later served as coach of Old Scotch, winning two premierships with the club.Phil Edwards (29 May 2014). "Sides commemorate players" – The Examiner. Retrieved 14 April 2015. A right-handed opening batsman, Harper made his first-class debut for Tasmania during the 1961–62 season, having been a regular participant in the annual North v. South fixture played between NTCA and TCA representative sides.Miscellaneous matches played by Barry Harper – CricketArchive. Retrieved 14 April 2015. On debut against Victoria in February 1962, he opened with Glen Waters, but was dismissed cheaply in each innings – leg before wicket to Ron Gaunt for one run in the first innings, and run out for five by Alan Connolly and Ray Jordon in the second.Tasmania v Victoria, Other First-Class matches in Australia 1961/62 – CricketArchive. Retrieved 14 April 2015. He scored 11 and 0 in the next match against South Australia at Adelaide Oval,South Australia v Tasmania, Other First-Class matches in Australia 1961/62 – CricketArchive. Retrieved 14 April 2015. but in the final game of the season against Victoria at Kardinia Park, Geelong, recorded his only first-class half-century.Victoria v Tasmania, Other First-Class matches in Australia 1961/62 – CricketArchive. Retrieved 14 April 2015. His innings of 58 runs was made in 230 minutes, and included only two fours.
