Fitzwater is a product of the West Bromwich Albion academy and was named academy player of the year for the 2014–15 season.
On 11 September 2015, Fitzwater signed on loan for Chesterfield for one month. He made his Football League debut for Chesterfield on 12 September 2015, coming on as a 19th-minute substitute for Gboly Ariyibi against Colchester United at the Proact Stadium. and was recalled by West Bromwich Albion on 3 January 2019. He returned for a third loan spell at Walsall on 31 January 2019.