Half-cut at university bar, knocked back Bloody Mary, say (5)
I believe the answer is:
tudor
'bloody mary say' is the definition.
(I know that Bloody Mary was a Tudor)
'half-cut at university bar knocked back' is the wordplay.
'half cut' indicates taking half.
'university' becomes 'U' (abbreviation for university).
'bar' becomes 'rod' (both can mean a pole or stick).
'knocked back' says the letters should be written backwards.
'rod' written backwards gives 'dor'.
'at' cut in half is 't'.
't'+'u'+'dor'='TUDOR'
(Other definitions for tudor that I've seen before include "Style of architecture in 15th century England" , "Elizabeth I, perhaps" , "Architectural style" , "Elizabeth I of England was of this royal family" , "Regal family" .)