Napier began his career in September 1963 playing for the Bolton Wanderers, where he played until 1967, when he was transferred to Brighton & Hove Albion for £25,000. He played until 1972 playing more than 200 games including two seasons as ever-present. In 1972, he was transferred to Bradford City for a record-equalling £10,000. He spent six seasons at Valley Parade interspersed with spells in America at Baltimore Comets and the same team after they became San Diego Jaws, and also at Mossley. In all he played more than 100 games at City, and served as manager, and assistant coach.
Napier served as manager at City from February 1978 to October 1978. He was unpopular as manager of Bradford City, as the team was relegated to the now-defunct Division Four. Napier returned to the United States in 1979 to take a coaching position at Pepperdine University, and continues to coach soccer.