Batty character? No artist, anyway (4)
I believe the answer is:
nora
'batty character? no artist anyway' is the definition.
I can't judge whether this defines the answer.
'batty character? no artist' is the wordplay.
'batty character?' becomes 'n' (I am not sure about the 'batty' bit.).
'no' becomes 'O' (resembles 0 - 'no' can mean 'zero').
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'n'+'o'+'ra'='NORA'
Can you help me to learn more?
(Other definitions for nora that I've seen before include "Woman" , "Girl's name" , "-- Batty (Last of the Summer Wine)" .)