In tears, after swilling Greek wine (7)
I believe the answer is:
retsina
'greek wine' is the definition.
(I've seen this before)
'in tears after swilling' is the wordplay.
'after' means one lot of letters go next to another.
'swilling' indicates anagramming the letters (swill can mean to stir or swirl round).
'in'+'tears'='intears'
'intears' is an anagram of 'RETSINA'.
(Other definitions for retsina that I've seen before include "S European wine" , "Greek resin-flavoured wine" , "Flavoured Greek white wine - nastier brand" , "Greek white wine flavoured with resin" , "Oily-tasting Greek white wine" .)