Unthinkable, a short part for the lead (5)
I believe the answer is:
Here is my best explanation:
'the lead' is the definition.
('leash' can be a synonym of 'lead')
'unthinkable a short part' is the wordplay.
'part' indicates the answer is hidden within the clue.
'LEASH' is hidden within 'unthinkable a short'.
'for' acts as a link.
(Other definitions for leash that I've seen before include "Rope to control dog", "Rope used to restrain an animal", "Bind", "A dog walker may use it", "Restraint for a dog", "Tether", "Rope or chain restraint", "Lead", "Spanish city famous for swordmaking" and "Restraining strap for dog".)