In despair, looking up, seeing part of church (4)
I believe the answer is:
apse
'part of church' is the definition.
('apse' is part of 'church')
'in despair looking up' is the wordplay.
'in' indicates a hidden word.
'looking up' shows that the letters should be reversed in order.
'espa' can be found hidden inside 'despair'.
'espa' reversed gives 'APSE'.
'seeing' is the link.
(Other definitions for apse that I've seen before include "Peas (anag) - found in church" , "Church recess in lapsed condition" , "may be seen in church!" , "space for altar" , "Niche in church" .)