Oliver joined the Munster Academy at the beginning of the 2015–16 season, having found his options limited with his native Leinster. On 19 February 2016, Oliver made his competitive debut for Munster when he came on as a replacement for Tommy O'Donnell against Glasgow Warriors in a 2015–16 Pro12 fixture. On 24 September 2016, Oliver scored his first try for Munster, having come on as a replacement for injured teammate Jack O'Donoghue in a 2016–17 Pro12 fixture against Edinburgh.