Artist's provided with injection of capital — all back to normal (8)
I believe the answer is:
familiar
'normal' is the definition.
(thesaurus)
'artist's provided with injection of capital all back' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'provided' becomes 'if'.
'with injection of' indicates putting letters inside (some letters injected in).
'capital' becomes 'lima' (capital of Peru).
'all back' shows that the letters should be reversed in order.
'ra'+'if'='raif'
'raif' going around 'lima' is 'railimaf'.
'railimaf' backwards is 'FAMILIAR'.
'to' is the link.
(Other definitions for familiar that I've seen before include "Well known or recognisable" , "Well-known; usual" , "Well-known, easily recognisable" , "spirit" , "Conversant with the witch's cat?" .)