Petty quarrel isn't quite severe (4)
I believe the answer is:
tiff
'petty quarrel' is the definition.
(I've seen this before)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for tiff that I've seen before include "A minor quarrel of disagreement" , "causing quarrel" , "(Lovers') quarrel" , "Lovers' row" , "A spat or small row" .)