Father interrupts street quarrel (4)
I believe the answer is:
spat
'quarrel' is the definition.
(spatting is a kind of quarrelling)
'father interrupts street' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'interrupts' is an insertion indicator.
'street' becomes 'st'.
'pa' put within 'st' is 'SPAT'.
(Other definitions for spat that I've seen before include "Row; discharged" , "Expelled" , "Taps in minor quarrel" , "angry words" , "Gestured with contempt" .)