Equality is hard in church district (6)
I believe the answer is:
parish
'church district' is the definition.
(I've seen this before)
'equality is hard' is the wordplay.
'equality' becomes 'par' ('par' can be a synonym of 'equality').
'hard' becomes 'h'.
'par'+'is'+'h'='PARISH'
'in' is the link.
(Other definitions for parish that I've seen before include "Administrative area within a diocese" , "Local church community" , "Local government area" , "area known to clergyman" , "Diocesan subdivision" .)