In general usage, heartless or artless girl (7)
I believe the answer is:
ingenue
'artless girl' is the definition.
(I've seen this before)
'in general usage heartless' is the wordplay.
'general' becomes 'gen'.
'heartless' suggests removing the centre.
'usage' with its centre taken out is 'ue'.
'in'+'gen'+'ue'='INGENUE'
'or' acts as a link.
(Other definitions for ingenue that I've seen before include "Unsophisticated young female" , "Genuine sort of young actress" , "Artless innocent young girl on stage" , "Unworldly young woman" , "Naive female" .)