Riddle of English graduate imbibing drink from east? (6)
I believe the answer is:
enigma
'riddle' is the definition.
('enigma' can be a synonym of 'riddle')
'english graduate imbibing drink from east?' is the wordplay.
'english' becomes 'e' (abbreviation).
'graduate' becomes 'ma' (abbreviation for Master of Arts).
'imbibing' means one lot of letters goes inside another.
'drink' becomes 'gin' (gin is a kind of drink**).
'from east?' is a reversal indicator (I've seen 'from East' mean this).
'gin' in reverse letter order is 'nig'.
'e'+'ma'='ema'
'ema' enclosing 'nig' is 'ENIGMA'.
'of' acts as a link.
(Other definitions for enigma that I've seen before include "German military cipher machine" , "'Puzzle, riddle (6)'" , "Riddle - German coding machine" , "Mysterious person" , "Puzzling person/thing" .)