On the French Riviera, trendy outsiders show a refined subtlety (6)
I believe the answer is:
nicety
'a refined subtlety' is the definition.
'nicety' can be an answer for 'subtlety' (synonyms). I'm unsure of the 'a refined' bit.
'on the french riviera trendy outsiders' is the wordplay.
'on' says to put letters next to each other.
'the french riviera' becomes 'nice' (I can't explain this - if you can you should give a lot more credence to this answer).
'outsiders' suggests removing the centre (only the letters on the outside of the word remain).
'trendy' with its middle taken out is 'ty'.
'nice' next to 'ty' is 'NICETY'.
'show' acts as a link.
Can you help me to learn more?
(Other definitions for nicety that I've seen before include "Fine point or subtlety" , "A detail of etiquette" , "Nuance - icy net (anag)" , "Finesse" , "Exactitude" .)