Flatter dairy product promoted (6,2)
I believe the answer is:
butter up
'flatter' is the definition.
(buttering up is a kind of flattering)
'dairy product promoted' is the wordplay.
'dairy product' becomes 'butter' (butter is a kind of dairy product).
'promoted' becomes 'up' (I've seen this in other clues).
'butter'+'up'='BUTTER UP'
(Other definitions for butter up that I've seen before include "Flatter for a purpose" , "Flatter with milk product?" , "Flatter in order to get something" , "like 17 [SWEET TALK]" , "Flatter to obtain favour" .)