Spirits after cold beer befuddled the brain (8)
I believe the answer is:
cerebrum
'brain' is the definition.
(I've seen this before)
'spirits after cold beer befuddled' is the wordplay.
'spirits' becomes 'rum' (rum is a kind of spirits).
'after' says to put letters next to each other.
'cold' becomes 'C' (eg on taps).
'befuddled' indicates an anagram.
'beer' with letters rearranged gives 'ereb'.
'c'+'ereb'='cereb'
'rum' after 'cereb' is 'CEREBRUM'.
'the' is the link.
(Other definitions for cerebrum that I've seen before include "Principal part of brain in front of skull" , "Main part of the brain" , "not a whole loaf?" , "Principle part of brain, in front of skull" , "One thinks" .)