European jazz fan, one raising quite a stink! (7)
I believe the answer is:
polecat
'one raising quite a stink' is the definition.
(smelly animal)
'european jazz fan' is the wordplay.
'european' becomes 'pole' (someone from Poland).
'jazz fan' becomes 'cat' (slang term for a jazz fan).
'pole'+'cat'='POLECAT'
(Other definitions for polecat that I've seen before include "Smelly American mammal" , "American skunk" , "Malodorous carnivore" , "Weasel-like mammal" , "weaselly type" .)