... perhaps eaten partly in recess? (4)
I believe the answer is:
apse
'recess?' is the definition.
(apse is a kind of recess)
'perhaps eaten partly in' is the wordplay.
'in' indicates the answer is hidden within the clue.
'APSE' is hidden within 'perhaps eaten partly'.
(Other definitions for apse that I've seen before include "Church recess in lapsed condition" , "inside church?" , "space for altar" , "Semicircular recess in church" , "Niche in church" .)