Eustace was born in Stocksbridge, West Riding of Yorkshire, and began his career as a trainee with Sheffield Wednesday. He made his debut in the 1962–63 season, and played more than 200 games in all competitions, before being sold to West Ham United for a club record £90,000 fee.
Eustace was born in Stocksbridge, West Riding of Yorkshire, and began his professional football career with Sheffield Wednesday. He made his debut in the 1962–63 season, playing over 200 games across all competitions before being transferred to West Ham United for a record-breaking £90,000 fee.