Artist great at painting, for example, the fashion business (3,5)
I believe the answer is:
rag trade
'the fashion business' is the definition.
(I've seen this before)
'artist great at painting for example' is the wordplay.
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'great at' becomes 'g' (I can't explain this - if you can you should believe this answer much more).
'painting for example' becomes 'trade' (painting is a kind of trade).
'ra'+'g'+'trade'='RAG TRADE'
Can you help me to learn more?
(Other definitions for rag trade that I've seen before include "Informally, the clothing business" , "Fashion industry (informal)" , "Informal description of clothing industry" , "Clothing business (colloq.)" , "National winner" .)