A model omitting old part of church (4)
I believe the answer is:
apse
'part of church' is the definition.
(part of a church building)
'a model omitting old' is the wordplay.
'model' becomes 'pose' (model can mean to pose).
'omitting' indicates named letters should be taken away.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'pose' with 'o' taken out is 'pse'.
'a'+'pse'='APSE'
(Other definitions for apse that I've seen before include "Where the altar is usually found in a church" , "Church's part" , "Where you could find a magistrate's chair" , "Primate holds saint to be a" , "Recess at east end of church" .)