Bust of upstart is in poor taste (6)
I believe the answer is:
statue
'bust' is the definition.
(I've seen this before)
'upstart is in poor taste' is the wordplay.
'upstart' becomes 'u' (start of the word 'up').
'is in' is an insertion indicator.
'poor' is an anagram indicator.
'taste' is an anagram of 'state'.
'u' going inside 'state' is 'STATUE'.
'of' acts as a link.
(Other definitions for statue that I've seen before include "As created by 3dn" , "Eg, the Venus de Milo" , "Artistic figure" , "Piece of sculpture" , "Stone figure" .)