Capital H for church district (6)
I believe the answer is:
parish
'church district' is the definition.
(I've seen this before)
'capital h' is the wordplay.
'capital' becomes 'paris' (Paris is an example).
'paris'+'h'='PARISH'
'for' is the link.
(Other definitions for parish that I've seen before include "administrative district" , "Ecclesiastical area" , "Local church community" , "Administrative area within a diocese" , "Rector's responsibility" .)