In extremis, alcoholic has drunk cola up in resort (8)
I believe the answer is:
acapulco
'resort' is the definition.
(Mexican resort)
'in extremis alcoholic has drunk cola up' is the wordplay.
'in extremis' suggests removing the centre (only the letters on the extremes are used).
'has' is a charade indicator (letters next to each other).
'drunk' indicates an anagram.
'alcoholic' with its middle removed is 'ac'.
'cola'+'up'='colaup'
'colaup' with letters rearranged gives 'apulco'.
'ac'+'apulco'='ACAPULCO'
'in' acts as a link.
(Other definitions for acapulco that I've seen before include "exotic holiday resort" , "Mexico port, resort" , "Mexican holiday destination" , "Mexican city" , "Mexican location" .)