Short dog with a trouble-free tail (4)
I believe the answer is:
curt
'short' is the definition.
(synonyms)
'dog with a trouble-free tail' is the wordplay.
'dog' becomes 'cur' (both can mean a despicable person).
'with' says to put letters next to each other.
'a trouble' becomes 'ail' (I've seen this before).
'free' is a deletion indicator.
'tail' with 'ail' removed is 't'.
'cur'+'t'='CURT'
(Other definitions for curt that I've seen before include "Brief and terse" , "Brusquely succinct" , "Brusque, abrupt in speech" , "Terse and laconic" , "Unceremonious" .)