Disagreement blows over? (4)
I believe the answer is:
spat
'disagreement' is the definition.
(spat is a kind of disagreement)
'blows over?' is the wordplay.
'blows' becomes 'taps' (tap is a kind of blow).
'over?' says the letters should be written in reverse (I've seen 'over ' mean this).
'taps' in reverse letter order is 'SPAT'.
(Other definitions for spat that I've seen before include "Taps in minor quarrel" , "Minor difference" , "Taps in a small quarrel" , "Short gaiter or slight quarrel (4)" , "Small altercations between Pats" .)