Irving quickly impressed during the club's pre-season and debuted for the first team on the opening day of the 1920–21 season in a 2–2 draw away at Falkirk on 16 August. He immediately established himself in the first team and scored his first goal for the side on 4 September in a victory over Falkirk. After receiving the ball, he advanced to the penalty area before shooting past the opposition goalkeeper, with the "Dundee Evening Telegraph" describing it as a "great goal". With the club struggling to fulfill their forward line, Irving moved from his traditional half back role to play as an outside right in November, although it was deemed unsuccessful by the "Dundee Courier" who noted that his presence was also missed from the half back line. His early season was later disrupted after missing several weeks of the season during the later months of 1920 after sustaining an injury against Airdrieonians. He made his return in December against Hamilton Academical. Irving helped the club to a fourth-placed finish in the 1920–21 Scottish Football League.