Arab artist appears in one quiz show (5)
I believe the answer is:
iraqi
'arab' is the definition.
(I've seen this before)
'artist appears in one quiz show' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'appears in' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'quiz show' becomes 'qi' (I can't explain this - if you can you should believe this answer much more).
'i'+'qi'='iqi'
'ra' inserted into 'iqi' is 'IRAQI'.
Can you help me to learn more?
(Other definitions for iraqi that I've seen before include "Native of Baghdad, say" , "Native of Fallujah, perhaps" , "Asian" , "Baghdad-born?" , "From Basra, possibly" .)