A very quiet artist is a learner being examined by supervisor? (9)
I believe the answer is:
appraisal
'being examined by supervisor?' is the definition.
(an assessment by one's employer)
'a very quiet artist is a learner' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'learner' becomes 'l' (as in a learner driver with L-plates on their car).
'a'+'pp'+'ra'+'is'+'a'+'l'='APPRAISAL'
(Other definitions for appraisal that I've seen before include "judgment" , "valuation" , "Evaluation - price survey" , "rating" , "Evaluation - papal airs (anag)" .)