Drink's on me, not Mike (3)
I believe the answer is:
one
'drink's' is the definition.
(eg 'a cold one')
'on me not mike' is the wordplay.
'not' suggests deleting specific letters.
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'me' with 'm' taken out is 'e'.
'on'+'e'='ONE'
(Other definitions for one that I've seen before include "Single, sole" , "Single and undivided" , "Sole; number" , "both halves" , "1" .)