One demands the best — often priciest — variety (13)
I believe the answer is:
perfectionist
'one demands the best' is the definition.
I can't judge whether this defines the answer.
'often priciest variety' is the wordplay.
'variety' indicates anagramming the letters.
'often'+'priciest'='oftenpriciest'
'oftenpriciest' with letters rearranged gives 'PERFECTIONIST'.
Can you help me to learn more?
(Other definitions for perfectionist that I've seen before include "One seeking the ideal" , "The Stickler" , "I expect the best" , "One aiming for the best" , "One striving for an ideal standard" .)