Star having drug and drink (9)
I believe the answer is:
sundowner
'drink' is the definition.
(sundowner is a kind of drink)
'star having drug' is the wordplay.
'star' becomes 'sun' (the Sun is a star).
'having' is a charade indicator (letters next to each other).
'drug' becomes 'downer' (downer is a kind of drug).
'sun'+'downer'='SUNDOWNER'
'and' is the link.
(Other definitions for sundowner that I've seen before include "Drink taken at the end of the day" , "Victorian tramp?" , "cocktail?" , "Evening drink" , "Tramp (Australian) - drink (British)" .)