Woman, certainly not an academician! (4)
I believe the answer is:
nora
'woman' is the definition.
(woman's name)
'certainly not an academician' is the wordplay.
'certainly not' becomes 'no'.
'an academician' becomes 'RA' (member of the Royal Academy of Arts).
'no'+'ra'='NORA'
(Other definitions for nora that I've seen before include "Woman" , "-- Batty (Last of the Summer Wine)" , "Girl's name" .)