Drunk kept a rum that's expensive (8)
I believe the answer is:
upmarket
'expensive' is the definition.
(I've seen this before)
'drunk kept a rum' is the wordplay.
'drunk' indicates an anagram.
'kept'+'a'+'rum'='keptarum'
'keptarum' anagrammed gives 'UPMARKET'.
'that's' is the link.
(Other definitions for upmarket that I've seen before include "for wealthy consumers" , "For the better off" , "Relatively expensive" , "Demanding higher prices" , "Aimed at those with money" .)