Charming involves branch (3)
I believe the answer is:
arm
'branch' is the definition.
(synonyms)
'charming involves' is the wordplay.
'involves' indicates the answer is hidden within the clue.
'ARM' is hidden within 'charming'.
(Other definitions for arm that I've seen before include "Body part" , "Equip with weapons" , "Shoulder-to-wrist member" , "Test of strength with elbows on the table" , "Authority" .)