District is equal to his conversion (6)
I believe the answer is:
parish
'district' is the definition.
(parish is a kind of district)
'equal to his conversion' is the wordplay.
'equal' becomes 'par'.
'conversion' indicates an anagram.
'his' is an anagram of 'ish'.
'par'+'ish'='PARISH'
'is' is the link.
(Other definitions for parish that I've seen before include "area known to clergyman" , "administrative district" , "Administrative area within a diocese" , "Area within diocese with own church" , "Unit of local government" .)