Anaesthetic given in pub (5)
I believe the answer is:
local
I believe this clue is a double definition.
'anaesthetic' is the first definition.
(local anaesthetic is a kind of anaesthetic)
'pub' is the second definition.
(one's local pub)
'given in' is the link.
(Other definitions for local that I've seen before include "Pub - of a particular area" , "Pub down the road?" , "nearest boozer!" , "Your friendly neighbourhood pub" , "bar" .)