Put up with jazz fan being an animal (7)
I believe the answer is:
bearcat
'an animal' is the definition.
(I've seen this before)
'put up with jazz fan' is the wordplay.
'put up with' becomes 'bear' (synonyms).
'jazz fan' becomes 'cat' (I've seen this in another clue).
'bear'+'cat'='BEARCAT'
'being' is the link.
(Other definitions for bearcat that I've seen before include "Animal" , "Cabaret (anag) - red panda" .)