Get rid of talking bird dipping into cream (9)
I believe the answer is:
eliminate
'get rid' is the definition.
(I've seen this before)
'talking bird dipping into cream' is the wordplay.
'talking bird' becomes 'mina' (bird which can imitate human speech).
'dipping into' means one lot of letters goes inside another.
'cream' becomes 'elite' (as in the cream of the crop).
'mina' going within 'elite' is 'ELIMINATE'.
'of' is the link.
(Other definitions for eliminate that I've seen before include "Completely remove, get rid of" , "Knock out" , "Do away with, remove" , "Reject" , "Wipe out" .)