A record for being drunk (4)
I believe the answer is:
high
I believe this clue is a double definition.
'a record' is the first definition.
(thesaurus)
'being drunk' is the second definition.
(I've seen this before)
'for' acts as a link.
(Other definitions for high that I've seen before include "At altitude" , "First-rate - drunk" , "Tall, elevated" , "Anticyclone; euphoric" , "(Of meat) slightly decomposed" .)