Obstinate fellow gets the slipper (4)
I believe the answer is:
mule
I believe this clue is a double definition.
'obstinate fellow' is the first definition.
'the slipper' is the second definition.
(mule is a kind of slipper)
'gets' acts as a link.
(Other definitions for mule that I've seen before include "Equine hybrid" , "Obstinate quadruped" , "Drug courier; animal" , "Hybrid beast" , "Hybrid animal - slipper" .)