Branch with a leaf if it mutated (9)
I believe the answer is:
affiliate
'branch' is the definition.
(I've seen this in another clue)
'a leaf if it mutated' is the wordplay.
'mutated' is an anagram indicator.
'leaf'+'if'+'it'='leafifit'
'leafifit' anagrammed gives 'ffiliate'.
'a'+'ffiliate'='AFFILIATE'
'with' acts as a link.
(Other definitions for affiliate that I've seen before include "Become closely connected" , "Associate with a parent body" , "Attach (to an organisation)" .)