Eat, in or out - see you shortly outside for a drink (9)
I believe the answer is:
cointreau
'a drink' is the definition.
(I've seen this before)
'eat in or out see you shortly outside' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'see' becomes 'c' (the word for the letter, according to Chambers**).
'shortly' indicates one should take the final letters.
'outside' is an insertion indicator.
The last letter of 'you' is 'u'.
'c'+'u'='cu'
'eat'+'in'+'or'='eatinor'
'eatinor' anagrammed gives 'ointrea'.
'ointrea' put into 'cu' is 'COINTREAU'.
'for' acts as a link.
(Other definitions for cointreau that I've seen before include "Sweet orange-flavoured colourless liqueur" , "Alcoholic drink" , "A sweet orange-flavoured liqueur for cautioner" , "Orange liqueur" .)