Part of church article intuition rejected (4)
I believe the answer is:
'part of church' is the definition.
(part of a church building)
'article intuition rejected' is the wordplay.
'article' becomes 'a' (the indefinite article in English).
'intuition' becomes 'ESP' (extra-sensory perception).
'rejected' shows that the letters should be reversed in order.
'esp' in reverse letter order is 'pse'.
(Other definitions for apse that I've seen before include "part of cathedral" , "Semicircular end of a church, behind the altar" , "place in church" , "Part of a church with the altar" , "Rounded end of building" .)