Argue over a name for member of the rose family (5)
I believe the answer is:
rowan
'member of the rose family' is the definition.
(tree of the rose family)
'argue over a name' is the wordplay.
'argue' becomes 'row' (to row with someone is to argue with them).
'over' is a charade indicator (letters next to each other).
'name' becomes 'n' (common abbreviation e.g. on forms).
'row'+'a'+'n'='ROWAN'
'for' is the link.
(Other definitions for rowan that I've seen before include "Tree bearing bright red berries" , "Atkinson or Williams" , "Mr Atkinson, actor" , "Mountain ash (at Lambeth!)" , "Tree with orange-red berry-like fruits" .)