Quiet enclosure in southern French island (7)
I believe the answer is:
silence
'quiet' is the definition.
('silence' can be a synonym of 'quiet')
'enclosure in southern french island' is the wordplay.
'enclosure' becomes 'enc'.
'in' means one lot of letters goes inside another.
'southern' becomes 's' (abbreviation).
'french island' becomes 'ile' (French for 'island').
's'+'ile'='sile'
'enc' inserted inside 'sile' is 'SILENCE'.
(Other definitions for silence that I've seen before include "License (anag)" , "Quiescence" , "may be required in court" , "Noiselessness" , "Quiet" .)