Be east of old tree (5)
I believe the answer is:
olive
'tree' is the definition.
(olive is a kind of tree)
'be east of old' is the wordplay.
'be' becomes 'live' (to be is to live or exist).
'east of' says to put letters next to each other (some letters go to the right of others).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'live' put after 'o' is 'OLIVE'.
(Other definitions for olive that I've seen before include "Fruit also used to make oil" , "It's branch is a symbol of peace" , "Its branch is a peace emblem" , "Evergreen Mediterranean tree" , "Yellow-green colour like Mediterranean fruit" .)