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' is an anagram indicator.
'ones' with letters rearranged 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" .)