A new leaf -- if it becomes a branch (9)
I believe the answer is:
affiliate
'a branch' is the definition.
(thesaurus)
'a new leaf if it' is the wordplay.
'new' indicates an anagram.
'leaf'+'if'+'it'='leafifit'
'leafifit' with letters rearranged gives 'ffiliate'.
'a'+'ffiliate'='AFFILIATE'
'becomes' 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)" .)