Drink has strangely thin base (8)
I believe the answer is:
absinthe
'drink' is the definition.
(absinthe is a kind of drink)
'strangely thin base' is the wordplay.
'strangely' indicates anagramming the letters.
'thin'+'base'='thinbase'
'thinbase' anagrammed gives 'ABSINTHE'.
'has' acts as a link.
(Other definitions for absinthe that I've seen before include "Potent aniseed-flavoured drink" , "Strong green liqueur, lethal when made with wormwood" , "Green aniseed liqueur" , "Potent green gin-type liquor - wormwood" , "French liqueur" .)