Possibly grips a branch (5)
I believe the answer is:
sprig
'a branch' is the definition.
(sprig is a kind of branch)
'possibly grips' is the wordplay.
'possibly' indicates an anagram.
'grips' is an anagram of 'SPRIG'.
(Other definitions for sprig that I've seen before include "A tack; a little shoot" , "Stem of holly, for example" , "Small spray of leaves or flowers" , "Tree shoot; headless nail" , "A child" .)