Old Bill, an artist, is a bit of a nut (5)
I believe the answer is:
copra
'a bit of a nut' is the definition.
(I've seen this before)
'old bill an artist' is the wordplay.
'old bill' becomes 'cop' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'an artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'cop'+'ra'='COPRA'
'is' acts as a link.
Can you help me to learn more?
(Other definitions for copra that I've seen before include "Dried coconut-kernel" , "Oil producer" , "Dried cocoa-nut kernels, source of oil" , "What gives oil" , "Shell offering oil" .)