Drink a politician offered, depending on chance (8)
I believe the answer is:
aleatory
'depending on chance' is the definition.
(aleatory means random or by chance)
'drink a politician' is the wordplay.
'drink' becomes 'ale' (type of beer).
'politician' becomes 'tory' (term for a Conservative Party politician).
'ale'+'a'+'tory'='ALEATORY'
'offered' is the link.
(Other definitions for aleatory that I've seen before include "dependent on chance" , "depending on chance" .)