Right-back Bradley has impressed since he joined from Dungannon Swifts in September 2019. He is already a full international having made his debut for Northern Ireland in a 3-0 friendly win in Malta at the age of 17 in May 2021. Bradley spent most of the 2020/21 season with Leeds' reserves. Bradley was rewarded for his progress when he made his first-team debut and kept a clean sheet in a 3-0 win at Norwich in the third round of the Carabao Cup on 21 September 2021. He went on to feature in the next two rounds of the competition as well as make a brief substitute appearance away to AC Milan in the Champions League, as well as start the 4th round home FA Cup tie against Shrewsbury, contributing with an assist in a 4-1 win.

League action in 2021/22 was confined to the Premier League 2, where Bradley scored twice and got eight assists, leading to a nomination for player of the season. Bradley spent the 2022/23 season on loan at League One Bolton where he was chosen as both Player of the Year and Players’ Player of the Year. Bradley signed a new contract at Liverpool on 1 December 2023. He blossomed in Liverpool's first team when deputising for the injured Trent Alexander-Arnold, scoring a stunning solo goal against Chelsea on 31 January 2024. By the end of the season he had played 23 games in all competitions, despite missing the first four months with a back injury. 

The 2024/25 season proved a mixed campaign for Conor Bradley, with injuries restricting his ability to establish himself as well as Slot's continued use of Trent Alexander-Arnold in his position. Operating as a right-back, Bradley had the talent and drive to contribute offensively and defensively, but recurring knocks meant he spent significant periods on the sidelines. Even in limited appearances, Bradley showed glimpses of his attacking instincts, making overlapping runs and delivering accurate crosses, while also demonstrating growing defensive awareness. A standout moment came against Real Madrid in a Champions League game at Anfield, when he raced back and dispossessed Kylian Mbappé with a perfect tackle, which was greeted with a roar as if Liverpool had scored a goal A fully fit Bradley could be an important option at right-back for Liverpool, competing directly with Jeremie Frimpong for a place in the side. Bradley signed a new four year deal in May 2025.