Disagreement blows up? (4)
I believe the answer is:
spat
'disagreement' is the definition.
(I know that spat is a type of dustup)
'blows up?' is the wordplay.
'blows' becomes 'taps' (tap is a kind of blow).
'up?' shows that the letters should be reversed in order (in down clue: letters go upwards).
'taps' written backwards gives 'SPAT'.
(Other definitions for spat that I've seen before include "Petty quarrel or fight" , "Reacted contemptuously" , "Observed" , "Slight argument" , "A small tiff or quarrel" .)