Second cat in bad air (4)
I believe the answer is:
smog
'bad air' is the definition.
(I've seen this in another clue)
'second cat' is the wordplay.
'second' becomes 's' (common abbreviation).
'cat' becomes 'mog' (informal British term).
's'+'mog'='SMOG'
'in' is the link.
(Other definitions for smog that I've seen before include "Industrially polluted air" , "Pollutant fog" , "Polluted haze" , "Polluted atmosphere" , "Pea-souper" .)