Feed on this, not that man's nipple! (4)
I believe the answer is:
teat
'nipple' is the definition.
(I know that nipple can be written as teat)
'feed on this not that man's' is the wordplay.
'feed on' becomes 'tea' (I can't justify this - if you can you should give a lot more credence to this answer).
'not' suggests deleting specific letters.
'that man's' becomes 'his' (belonging to a man).
'this' with 'his' taken out is 't'.
'tea'+'t'='TEAT'
Can you help me to learn more?
(Other definitions for teat that I've seen before include "Bulb on infant's bottle" , "Nipple or dug" , "Piece on baby's bottle" , "essential for babies" , "Part of feeding bottle" .)