Playing in particular as a right back, Rice was initially a bit-part player, making only 16 appearances in his first three seasons at Arsenal. He also went on to miss out on Arsenal's 1969–70 Inter-Cities Fairs Cup win over RSC Anderlecht. However, during this time he won his first cap for Northern Ireland, against Israel on 10 September 1968, while still largely a reserve player. Peter Storey was Arsenal's first choice right back, but he was soon moved into central midfield at the start of the 1970–71 season. With this being so, Rice took his place and was a near-ever present figure in the side of that season, as Arsenal won the League and FA Cup Double.