Owl, dropping wings, lands in chestnut tree (5)
I believe the answer is:
rowan
'tree' is the definition.
(rowan tree is a kind of tree)
'owl dropping wings lands in chestnut' is the wordplay.
'dropping wings' says to take the centre.
'lands in' indicates putting letters inside.
'chestnut' becomes 'roan' (as in a roan horse).
The middle of 'owl' is 'w'.
'w' going into 'roan' is 'ROWAN'.
(Other definitions for rowan that I've seen before include "Tree - archbishop" , "Sort of ash" , "Tree with orange-red berry-like fruits" , "Mountain ash (at Lambeth!)" , "Atkinson or Williams" .)