Climbing around branch (4)
I believe the answer is:
limb
'branch' is the definition.
(I've seen this in another clue)
'climbing around' is the wordplay.
'around' indicates the answer is hidden within the clue.
'LIMB' is hidden within 'climbing'.
(Other definitions for limb that I've seen before include "Substantial branch from a tree trunk" , "Eg, arm, leg" , "Tentacle" , "Branch - member" , "as part of plane, say" .)