Has run around tree (3)
I believe the answer is:
ash
'tree' is the definition.
(ash is a kind of tree)
'has run' is the wordplay.
'run' indicates an anagram.
'has' anagrammed gives 'ASH'.
'around' acts as a link.
(Other definitions for ash that I've seen before include "Remains of conflagration" , "Get the residue" , "Burnt material; tree" , "Part of forest" , "remains after forest fire?" .)