Quansah who has been raised in Liverpool's academy system since age seven is a towering centre-half. Quansah was loaned to Bristol Rovers for the second half of 2022/23, making fifteen starts in League One. He made his first-team debut in a 2-1 win at Newcastle on 27 August 2023 after centre-half Virgil Van Dijk had been sent off. Quansah replaced Joel Matip in the 77th minute, partnering with Joe Gomez. In doing so, he became the first player whose surname began with a Q to play for Liverpool. 

During the season Quansah demonstrated why the club had not bought a centre back the previous summer. He was strong at the back, good in the air and carried the ball forward confidently. He made 31 appearances in all competitions, scoring three goals. For the last six Premier League games Quansah displaced Konate as Van Dijk's central defensive partner and was called up to the initial England squad for Euro 24. However, after being an unused substitute in the two warm-up games he failed to make the final 26.

Quansah had a difficult start to the 2024/25 season. He was substituted at half time on the opening day at Ipswich, new head coach citing him not winning enough duels. He started just three more Premier League games all season, two of them after the title had been secured. Quansah played every minute of England Under 21's European Championship success in the summer. He was sold to Bayer Leverkusen on 2 July 2025, the German club paying a £30m initial fee with £5m add-ons. Liverpool inserted a buy-back clause starting from €60m plus add-ons available from 2027.