Fast to get under the influence (5)
I believe the answer is:
tight
I believe this is a double definition.
'fast' is the first definition.
(I know that fast can be written as tight)
'under the influence' is the second definition.
(thesaurus)
'to get' is the link.
(Other definitions for tight that I've seen before include "Bottled ," , "Inebriated" , "Mean - drunk" , "Hard to move; drunk" , "Miserly (informal) - drunk (informal)" .)