He attended school at Tupton Hall, alongside future Labour MP Dennis Skinner.
He began his professional career in February 1950 with Chesterfield, whom he joined as an amateur from Clay Lane Sports Club in 1948.
Leivers moved to Manchester City in November 1953, for a fee of £10,500,[2] making his debut against Preston North End in August 1954.
Though he was known as a centre half when he arrived at Maine Road, it was at right-back that he established himself in the Manchester City team, during the 1955–56 season.
With the death of Roy Little in January 2015, Leivers is the last-living player from the Manchester City 1956 FA Cup winning squad.