After a loan spell at Peterborough United, Price broke into the Arsenal first team in 1977–78, playing 51 matches that season. This was noteworthy as he had previously made only 13 appearances for the club. His regular spell in the Arsenal side coincided with the Gunners' FA Cup runs of the late 1970s, where they consecutively got to the 1978 to 1980 finals of the cup. Price thus played three times at Wembley with Arsenal winning the 1979 FA Cup in a 3–2 win against Manchester United. Price got an assist in the game as he set up Brian Talbot for the opening goal. Price also played in Arsenal's 1980 Cup Winners' Cup defeat at the hands of Valencia, on penalties.