Short dog with a little tail (4)
I believe the answer is:
curt
'short' is the definition.
(I know that short can be written as curt)
'dog with a little tail' is the wordplay.
'dog' becomes 'cur' (both can mean a despicable person).
'with' is a charade indicator (letters next to each other).
'a little' indicates taking the first letters.
The initial letter of 'tail' is 't'.
'cur'+'t'='CURT'
(Other definitions for curt that I've seen before include "Brief and terse" , "Brusque, short" , "Snappy" , "Brusque, abrupt in speech" , "Concise" .)