Respectable church beset by depression (6)
I believe the answer is:
decent
'respectable' is the definition.
('decent' can be similar in meaning to 'respectable')
'church beset by depression' is the wordplay.
'church' becomes 'ce' (abbreviation for Church of England).
'beset by' means one lot of letters goes inside another ('beset' could historically mean 'cover').
'depression' becomes 'dent' ('dent' can be a synonym of 'depression').
'ce' put within 'dent' is 'DECENT'.
(Other definitions for decent that I've seen before include "Honest and modest" , "Proper and suitable" , "Appropriate, fitting" , "Modest or kind" , "Adequately covered" .)