Half-cut at university bar, knocked back Bloody Mary, say (5)
I believe the answer is:
'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'.
(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" .)