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