Inside-left Wallace had been an apprentice at Anfield before signing professional forms for the club in July 1961, a month after his seventeenth birthday. He had to wait until the end of October 1962 before Shankly gave him his first-team debut and he was picked on a further six occasions by the end of that season, the club's first back in the top division after an eight-year absence. A year later, when Liverpool won the League Championship for the first time since 1947, no fewer than ten men made at least 33 League appearances and Wallace's only League game came at Burnley towards the end of the season, when he replaced the injured Roger Hunt. Wallace was the toast of the town in an eight-day period in the 1964/65 season when he scored five goals. He scored once when Liverpool drew 2-2 with West Ham in the Charity Shield and then made history when he scored Liverpool's first goal in a European competition in Reykjavik in the third minute adding another after an hour's play. Wallace scored twice at Anfield against Arsenal on the opening day of the 1964/65 league season, the first-ever game covered by the BBC as their "Match of the Day". He made the team for the first eight matches of that campaign but following three consecutive defeats Shankly brought in Bobby Graham in his place and Wallace had to wait over five months for his next League outing. Wallace didn't use his extended run in the side to its fullest capability and called it quits at Anfield in October 1967 after a succession of injuries and two frustrating years in Liverpool's reserve team. He went on to make just over 100 appearances in five years at fourth division Crewe, scoring 22 goals.