Wife stuck in chestnut tree (5)
I believe the answer is:
rowan
'tree' is the definition.
(rowan tree is a kind of tree)
'wife stuck in chestnut' is the wordplay.
'wife' becomes 'w'.
'stuck in' is an insertion indicator.
'chestnut' becomes 'roan' (as in a roan horse).
'w' inserted within 'roan' is 'ROWAN'.
(Other definitions for rowan that I've seen before include "Tree - archbishop" , "Tree with orange-red berry-like fruits" , "Mr Atkinson, actor" , "Man" , "Sort of ash" .)