Remnant of broken bust (4)
I believe the answer is:
stub
'remnant' is the definition.
(I've seen this in another clue)
'broken bust' is the wordplay.
'broken' indicates an anagram.
'bust' with letters rearranged gives 'STUB'.
'of' acts as a link.
(Other definitions for stub that I've seen before include "Strike one's toe accidentally (against something)" , "Tooth remnant" , "Possible proof of journey" , "Short bit of pencil, say" , "Bust (anag.)" .)