Close to being sozzled? (5)
I believe the answer is:
tight
I believe this is a double definition.
'close' is the first definition.
(I know that close can be written as tight)
'being sozzled?' is the second definition.
(synonyms)
'to' is the link.
(Other definitions for tight that I've seen before include "Firmly fastened; drunk" , "happy" , "Close-fitting; cramped; mean" , "Miserly (informal) - drunk (informal)" , "Rigid; drunk" .)