Branch grasped by climber (4)
I believe the answer is:
limb
'branch' is the definition.
(I know that limb is a type of branch)
'grasped by climber' is the wordplay.
'grasped by' says the answer is hidden in the clue.
'LIMB' is hidden in the letters of 'climber'.
(Other definitions for limb that I've seen before include "Arm, leg or wing" , "Jointed appendage" , "Branch - member" , "Human's extension" , "Tentacle" .)