One casual affair on a party island (5)
I believe the answer is:
ibiza
'island' is the definition.
(Spanish island)
'one casual affair on a' is the wordplay.
'one' becomes 'i' (Roman numeral).
'casual affair' becomes 'biz' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'i'+'biz'+'a'='IBIZA'
'party' is the link.
Can you help me to learn more?
(Other definitions for ibiza that I've seen before include "holiday destination" , "Island in the Balearics" , "Westermost of Balearic Islands, popular for holidays" , "part of Spain" , "part of the Balearics" .)