City suppressing anything bad (7)
I believe the answer is:
naughty
'bad' is the definition.
('naughty' can be similar in meaning to 'bad')
'city suppressing anything' is the wordplay.
'city' becomes 'ny' (I've seen this in other clues**).
'suppressing' is an insertion indicator.
'anything' becomes 'aught' (I've seen this before).
'ny' going around 'aught' is 'NAUGHTY'.
(Other definitions for naughty that I've seen before include "Mischievous - improper" , "Dubious" , "Badly behaved, mischievous" , "Behaving badly or risque" , "Badly-behaved" .)