Winger Doak signed from Celtic in the summer of 2022 and the 16-year-old only made his first team debut five months later. He had already featured for 25 minutes in two Premiership games for Celtic before his move south. Klopp was impressed with Doak's Anfield debut against Derby County in the League Cup: “His instructions were easy: do what you do all the time. He’s really a lively boy, a smart player, good dribbler, fast, can use both legs. He’s good! It was nice to watch, eh? It was really nice to watch, him coming in and immediately a lot of things are obviously natural to him, which is really helpful. I’m pretty sure his family was here tonight. I can remember when I saw the family at the AXA when we signed the boy, how excited everybody was," Klopp concluded.

Doak made two substitute appearances in the Premier League in 2022/23. He then came off the bench at Chelsea in the opening game of 2023/24. There were high expectations for the season ahead with plenty of opportunities expected in the cups. He started three of Liverpool's six group games in the Europa League, but was ruled out for the rest of the season after a cartilage injury sustained in December. Doak was surprisingly called up to Scotland's initial squad for Euro 2024, with manager Steve Clarke saying he offered pace that others didn't. However, an injury sustained in training led to his withdrawal after just a few days. Doak was loaned to Middlesbrough for 2024/25 and impressed, with three goals and seven assists in 24 appearances prior to picking up a thigh injury in January. He also made six appearances for Scotland in the UEFA Nations League. He underwent surgery in March 2025 and remained with Liverpool for his rehabilitation. Doak was sold to Bournemouth for £25 million on 18 August 2025.