Brad joined the Rhinos in 2018 from Warrington Wolves on a two-year contract. He made his first Rhinos appearance in the Festive Challenge against Wakefield and made his debut off the bench on the opening day of the season against Warrington before going onto appear in his first World club challenge against Melbourne.
He registered eight tries in 23 appearances and became a crowd favourite in his first season at Emerald Headingley. The hooker has previously played at Huddersfield and London on loan from the Wolves and has been at the Halliwell Jones Stadium since making his debut in 2012 against Wakefield. In his first season with Warrington he registered three tries in eight appearances, the first coming against Catalans Dragons.
In 2013 he featured four times from the bench for Warrington and spent a month on loan with Huddersfield, where he played a further six times. He returned to Warrington in 2014 and signed a new two-year contract, before playing ten times for the club as the team made it through to the semi-final of the Challenge Cup and play offs.
During the 2015 season Dwyer played 19 times for Warrington and appeared nine times for London Broncos during a loan period with the Championship Club. In 2016 he earned a regular first team place for Warrington making 23 appearances and winning the League Leaders Shield.