Gin cocktail swallowed by rising star in French city (7)
I believe the answer is:
avignon
'french city' is the definition.
(I've seen this before)
'gin cocktail swallowed by rising star' is the wordplay.
'cocktail' is an anagram indicator.
'swallowed by' is an insertion indicator.
'rising' says the letters should be written in reverse (going up in a down clue).
'star' becomes 'nova' (nova is a kind of star**).
'nova' written backwards gives 'avon'.
'gin' anagrammed gives 'ign'.
'ign' inserted within 'avon' is 'AVIGNON'.
'in' acts as a link.
(Other definitions for avignon that I've seen before include "European city" , "Provence city" , "French town with a 17 dn mentioned in song" , "where bridge is noted" , "French city, once seat of Popes" .)