Start to speak, swallowing current drink (9)
I believe the answer is:
originate
'start' is the definition.
(I know that start can be written as originate)
'speak swallowing current drink' is the wordplay.
'speak' becomes 'orate' (orating is a kind of speaking).
'swallowing' means one lot of letters goes inside another.
'current' becomes 'I' (symbol for electric current).
'drink' becomes 'gin' (gin is a kind of drink).
'i'+'gin'='igin'
'orate' placed around 'igin' is 'ORIGINATE'.
'to' acts as a link.
(Other definitions for originate that I've seen before include "Bring into existence" , "Create, initiate" , "From kick off" , "issue" , "Arise, start" .)