Start to make a speech having swallowed one drink (9)
I believe the answer is:
originate
'start' is the definition.
('originate' can be a synonym of 'start')
'make a speech having swallowed one drink' is the wordplay.
'make a speech' becomes 'orate' (I've seen this before).
'having swallowed' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'drink' becomes 'gin' (gin is a kind of drink).
'i'+'gin'='igin'
'orate' enclosing 'igin' is 'ORIGINATE'.
'to' acts as a link.
(Other definitions for originate that I've seen before include "In spring" , "Invent" , "Found" , "pioneer" , "issue" .)