 Eastham's time at Arsenal was often turbulent; as well as the court case against Newcastle United, he fell out with Arsenal after asking for a pay rise following the maximum wage's abolishment in 1961 (but eventually Arsenal relented and met his demands), and he asked for a transfer after being replaced by Joe Baker up front at the start of the 1962–63 season.However, Billy Wright sought a compromise and eventually restored Eastham to the side, behind Baker; Eastham's form returned, he came off the transfer list and in both 1963–64 and 1964–65 he scored ten goals, the most per season during his Arsenal career, which included two in a 4–4 draw in a memorable North London derby match against Tottenham Hotspur at Highbury in October 1963.It was at Arsenal that Eastham's international career flourished; he joined the England squad for the 1962 FIFA World Cup as an uncapped player, but did not play in the tournament; his England debut finally came on 8 May 1963, against Brazil.