Gently persuade to announce drinks (4)
I believe the answer is:
coax
'gently persuade' is the definition.
(I've seen this before)
'announce drinks' is the wordplay.
'announce' indicates a 'sounds like' (homophone) clue.
'drinks' becomes 'cokes' (Coke is an example).
'cokes' sounds like 'COAX'.
'to' is the link.
(Other definitions for coax that I've seen before include "Get round" , "sort of cable" , "Gently persuade" , "Wheedle, cajole" , "Carefully manipulate" .)