'One more Cinzano', the rector's drunk (7)
I believe the answer is:
another
'one more' is the definition.
(I've seen this before)
'cinzano the rector's drunk' is the wordplay.
'drunk' indicates a hidden word (it was drunk by the letters so within them).
'ANOTHER' can be found hidden inside 'cinzano the rectors'.
(Other definitions for another that I've seen before include "A different (thing)" , "A further (item)" , "Additional: alternative" , "On earth (anag.)" , "encore?" .)