First using mouth to swallow one drink (10)
I believe the answer is:
originally
'first' is the definition.
(I've seen this before)
'using mouth to swallow one drink' is the wordplay.
'using mouth' becomes 'orally' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'to swallow' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'drink' becomes 'gin' (gin is a kind of drink).
'i'+'gin'='igin'
'orally' placed around 'igin' is 'ORIGINALLY'.
Can you help me to learn more?
(Other definitions for originally that I've seen before include "to begin with" , "At the start" , "In the first place" , "new way" .)