Routine suggestion given to artist (3,4)
I believe the answer is:
rat race
'routine' is the definition.
(rat race is a kind of routine)
'suggestion given to artist' is the wordplay.
'suggestion' becomes 'trace' ('trace' can be a synonym of 'suggestion').
'given to' is a charade indicator (letters next to each other).
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'trace' after 'ra' is 'RAT RACE'.
(Other definitions for rat race that I've seen before include "Struggle for necessities" , "Continual routine of highly competitive activity" , "Competitive way of life" , "The competitive society" , "Competitive daily existence" .)