Stiffly have an argument (4)
I believe the answer is:
tiff
'an argument' is the definition.
(I know that tiff is a type of dustup)
'stiffly have' is the wordplay.
'have' indicates a hidden word.
'TIFF' can be found hidden inside 'stiffly'.
(Other definitions for tiff that I've seen before include "Row; argument" , "Slight quarrel" , "A petty quarrel or difference" , "Minor squabble" , "Hard to lose opening argument" .)