This girl owns up about artist (5)
I believe the answer is:
sarah
'this girl' is the definition.
'owns up about artist' is the wordplay.
'owns' becomes 'has' ('have' can be a synonym of 'own').
'up' says the letters should be written backwards (in down clue: letters go upwards).
'about' means one lot of letters goes inside another.
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'has' backwards is 'sah'.
'sah' placed around 'ra' is 'SARAH'.
(Other definitions for sarah that I've seen before include "Girl" , "Abraham's wife in the Old Testament" , "Abraham's wife (OT)" , "Girl's name" , "Lady" .)