Part of church any parishioners should examine initially (4)
I believe the answer is:
apse
'part of church' is the definition.
(part of a church building)
'any parishioners should examine initially' is the wordplay.
'initially' says to take the initial letters.
The first letters of 'any parishioners should examine' is 'APSE'.
(Other definitions for apse that I've seen before include "Projection to the east end of a church" , "Niche in church" , "Church recess with domed or arched roof" , "space for altar" , "Recess at east end of church" .)