Period piece finally put before artist (3)
I believe the answer is:
era
'period' is the definition.
(era is a kind of period)
'piece finally put before artist' is the wordplay.
'finally' suggests the final letters.
'put before' is a charade indicator (letters next to each other).
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
The last letter of 'piece' is 'e'.
'e'+'ra'='ERA'
(Other definitions for era that I've seen before include "Important time" , "Geological age" , "quite some time" , "generation, maybe" , "Stage" .)