Disagreement over a new tree (5)
I believe the answer is:
rowan
'tree' is the definition.
(type of tree)
'disagreement over a new' is the wordplay.
'disagreement' becomes 'row' (row is a kind of disagreement).
'over' says to put letters next to each other (in a down clue, some letters go over others).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'row'+'a'+'n'='ROWAN'
(Other definitions for rowan that I've seen before include "Canterbury" , "Mountain ash (at Lambeth!)" , "Tree - archbishop" , "Mountain-ash" , "Tree bearing bright red berries" .)