Something Woody occasionally targeted (4)
I believe the answer is:
tree
'something woody' is the definition.
(trees have wood)
'occasionally targeted' is the wordplay.
'occasionally' means one should take alternating letters.
The alternate letters of 'targeted' are 'TREE'.
(Other definitions for tree that I've seen before include "eg Box" , "Root-and-branch plant?" , "eg Cedar" , "Chestnut or elm?" , "Genealogist's work" .)