Branch in Slimbridge (4)
I believe the answer is:
'branch' is the definition.
(I know that branch can be written as limb)
'in slimbridge' is the wordplay.
'in' indicates the answer is hidden within the clue.
'LIMB' can be found hidden inside 'slimbridge'.
(Other definitions for limb that I've seen before include "Human's extension" , "Tentacle" , "as part of plane, say" , "arm, perhaps" , "A supporter" .)