Not oddly worried after controversial coat causes uproar (6)
I believe the answer is:
furore
'uproar' is the definition.
(synonyms)
'not oddly worried after controversial coat' is the wordplay.
'not oddly' indicates alternate letters (odd letters are removed).
'after' is a charade indicator (letters next to each other).
'controversial coat' becomes 'fur' (some object to animals being killed for their fur).
The alternating letters of 'worried' are 'ore'.
'ore' after 'fur' is 'FURORE'.
'causes' is the link.
(Other definitions for furore that I've seen before include "An uproar, of admiration or anger" , "'Uproar, brouhaha (6)'" , "Frenzied excitement, uproar" , "Noisy state of wild confusion" , "Hoo-ha" .)