As drunk by Joe at the Nag's Head (3)

I believe the answer is:
gin
'as drunk' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how one could define the other.
'joe at the nag's head' is the wordplay.
'joe' becomes 'GI' (GI Joe).
'at' says to put letters next to each other.
'head' says to take the initial letters.
The initial letter of 'nags' is 'n'.
'gi'+'n'='GIN'
'by' is the link.
Can you help me to learn more?
(Other definitions for gin that I've seen before include "Strong drink - trap" , "Machine for separating cotton from its seeds" , "Trap; mother's ruin" , "It often gets mixed up with this" , "Alcoholic drink made from juniper berries - it's a trap" .)
