Slight quarrel over some gauzy fabric (7)
I believe the answer is:
tiffany
'gauzy fabric' is the definition.
(I've seen this before)
'slight quarrel over some' is the wordplay.
'slight quarrel' becomes 'tiff' (I've seen this before).
'over' is a charade indicator (letters next to each other) (in a down clue, some letters go over others).
'some' becomes 'any' (similar in meaning).
'tiff'+'any'='TIFFANY'
(Other definitions for tiffany that I've seen before include "fine fabric" , "US glass designer" , "Girl's name - New York jeweller" , "gauzy fabric" , "like a sort of glass" .)