Harry joined Liverpool as an Under-9 and made his youth team debut as an Under-16 during the 2012-13 campaign. A tricky and pacey left winger, he was a regular as a first-year scholar the following year, topping the goalscoring chart for his age group with 14 goals. The 2014-15 season saw him make the step up to the Under-21s, playing 14 games and scoring six goals, while also playing ten games and scoring eleven goals for the Under-18s. The Welshman continued to catch the eye, notably scoring late winners against local rivals Everton and against Real Madrid in the UEFA Youth League, and was rewarded for an impressive campaign by being shortlisted for the Barclays U21 Player of the Season award. On 11 July, 2015, it was announced that he would join Liverpool's first team on their pre-season tour of Thailand, Australia and Malaysia. On 16 August, he was crowned best forward of the prestigious PSV Otten Cup. On 26 August, it was confirmed that he had joined Crewe Alex on a youth loan until January.
Harry was made Under-23s captain for the 2016-17 season and made his first-team debut in an FA Cup tie against Plymouth Argyle on January 18 2017.