Curate's parents hold up part of the church (4)
I believe the answer is:
apse
'part of the church' is the definition.
(part of a church building)
'curate's parents hold up' is the wordplay.
'hold' indicates the answer is hidden within the clue (I've seen 'holding' mean this).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'espa' is hidden within 'curates parents'.
'espa' back-to-front is 'APSE'.
(Other definitions for apse that I've seen before include "Recess at east end of church" , "Architectural feature in a church" , "In sacred space" , "space for altar" , "Offshoot from the choir, nave or aisle in a church" .)