Stubborn, small pet (5)
I believe the answer is:
'stubborn' is the definition.
'small pet' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'pet' becomes 'tiff' (I've seen this before).
(Other definitions for stiff that I've seen before include "Rigid, unbending", "cheat", "Unyielding", "Formal", "Awkward".)