Backing ID check for each complaint (9)
I believe the answer is:
distemper
'complaint' is the definition.
(distemper is a kind of disease)
'backing id check for each' is the wordplay.
'backing' says the letters should be written in reverse.
'check' becomes 'stem' (both can mean to control or stop).
'for each' becomes 'per' (per person).
'id' in reverse letter order is 'di'.
'di'+'stem'+'per'='DISTEMPER'
(Other definitions for distemper that I've seen before include "problem for pet" , "Viral disease" , "Infectious disease of animals" , "Colourful coat" , "Viral infection < found in lab" .)