Drunk Nads downing last drop of absinthe in American saloon (5)
I believe the answer is:
sedan
'american saloon' is the definition.
(US term for a saloon car)
'drunk nads downing last drop of absinthe' is the wordplay.
'drunk' is an anagram indicator.
'downing' means one lot of letters goes inside another (to down food or drink is to swallow it quickly).
'last drop of' indicates one should take the final letters.
The last letter of 'absinthe' is 'e'.
'nads' is an anagram of 'sdan'.
'sdan' placed around 'e' is 'SEDAN'.
'in' is the link.
(Other definitions for sedan that I've seen before include "Type of chair - battle" , "outmoded form of transport" , "Saloon car (US)" , "Old carrier chair for Danes" , "Type of chair that's carried" .)