Bugs turned up, provoking petty quarrel (4)
I believe the answer is:
spat
'petty quarrel' is the definition.
(I've seen this before)
'bugs turned up' is the wordplay.
'bugs' becomes 'taps' ('tap' can be a synonym of 'bug').
'turned up' shows that the letters should be reversed in order.
'taps' reversed gives 'SPAT'.
'provoking' acts as a link.
(Other definitions for spat that I've seen before include "Trivial quarrel" , "Small quarrel between Pats" , "A small tiff or quarrel" , "Showed contempt" , "A minor dispute or row" .)