Hung over, embracing second American to a large extent (9)
I believe the answer is:
humongous
'to a large extent' is the definition.
'hung over embracing second american' is the wordplay.
'hung over' becomes 'hung' ('hang' can be a synonym of 'hang over').
'embracing' means one lot of letters goes inside another.
'second' becomes 'mo' (both are short periods of time).
'american' becomes 'ous' (I can't explain this - if you can you should believe this answer much more).
'hung' placed around 'mo' is 'humong'.
'humong'+'ous'='HUMONGOUS'
(Other definitions for humongous that I've seen before include "Huge" , "Titanic" , "Very large" .)