Dispute ignoring opening of firm (4)
I believe the answer is:
tiff
'dispute' is the definition.
(tiff is a kind of dispute)
'ignoring opening of firm' is the wordplay.
'ignoring opening of' means to remove the first letter.
'firm' becomes 'stiff' (I've seen this before).
'stiff' with its initial letter taken away is 'TIFF'.
(Other definitions for tiff that I've seen before include "Quarrel (colloq.)" , "Minor squabble" , "Mild quarrel" , "A minor quarrel of disagreement" , "Slight quarrel" .)