Absent-minded copper's distinguishing feature (8)
I believe the answer is:
distrait
'absent-minded' is the definition.
(I've seen this before)
'copper's distinguishing feature' is the wordplay.
'copper's' becomes 'dis' (detective inspector, type of copper).
'distinguishing feature' becomes 'trait' (I've seen this before).
'dis'+'trait'='DISTRAIT'
(Other definitions for distrait that I've seen before include "Distraught in France" , "Preoccupied" , "Unable to concentrate for anxiety - it is trad (anag)" , "Inattentive or absent-minded, from French" , "Being one [SCATTY]" .)