Kate's wandering in the wood (4)
I believe the answer is:
teak
'wood' is the definition.
(type of timber)
'kate's wandering' is the wordplay.
'wandering' indicates an anagram.
'kate' is an anagram of 'TEAK'.
'in the' is the link.
(Other definitions for teak that I've seen before include "E. Indies hardwood" , "Hard wood for Kate" , "Hard wood used for furniture" , "Hard durable timber" , "Take away with very hard wood" .)