Organ one’s broken (4)
I believe the answer is:
nose
'organ' is the definition.
(nose is a kind of organ)
'one's broken' is the wordplay.
'broken' indicates an anagram.
'ones' anagrammed gives 'NOSE'.
(Other definitions for nose that I've seen before include "Asian wind instrument -- use Teflon (anag)" , "Deserving blame" , "Olafactory organ" , "Aroma of wine" , "Schnozzle" .)