In short, a mongrel has not much of a tail (4)
I believe the answer is:
curt
'in short' is the definition.
'curt' can be an answer for 'short' (synonyms). I am unsure of the 'in' bit.
'a mongrel has not much of a tail' is the wordplay.
I cannot really understand how this works, but
'mongrel' could be 'cur' (synonyms) and 'cur' is present in the answer.
A single letter 't' remains which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for curt that I've seen before include "Brusque, short" , "Terse and laconic" , "Unceremonious" , "Brief and terse" , "Rudely brief" .)