Me drunk with a gin? It's puzzling! (6)
I believe the answer is:
enigma
'it's puzzling' is the definition.
(I've seen this in another clue)
'me drunk with a gin?' is the wordplay.
'drunk with' is an anagram indicator.
'a'+'gin'='agin'
'me' mixed up with 'agin' makes 'ENIGMA'.
(Other definitions for enigma that I've seen before include "Mysterious person" , "Coding device" , "Puzzle found in gem, Ian" , "Gamine being a bit of a puzzle" , "Riddle - German coding machine" .)