The horrid ref's playing for County (13)
I believe the answer is:
hertfordshire
'county' is the definition.
(I know that Hertfordshire is a county)
'the horrid ref's playing' is the wordplay.
'playing' indicates an anagram.
'the'+'horrid'+'refs'='thehorridrefs'
'thehorridrefs' is an anagram of 'HERTFORDSHIRE'.
'for' is the link.
(Other definitions for hertfordshire that I've seen before include "County of Watford and Ware" , "Southern county" , "A home county" , "Watford's county" , "County to N. of London" .)