Cocktail from Caribbean island that Parisian avoids (7)
I believe the answer is:
martini
'cocktail' is the definition.
(I know that Martini is a type of cocktail)
'caribbean island that parisian avoids' is the wordplay.
'caribbean island' becomes 'martinique' (island of the Lesser Antilles).
'that parisian' becomes 'que' ('that' in French).
'avoids' suggests deleting specific letters.
'martinique' with 'que' taken away is 'MARTINI'.
'from' acts as a link.
(Other definitions for martini that I've seen before include "rifle" , "James Bond's drink of choice" , "Cocktail made with gin or vodka and vermouth" , "Type of Italian vermouth" , "obtained from a bottle" .)