Take on a variety of muses (6)
I believe the answer is:
assume
'take on' is the definition.
(I know that take on can be written as assume)
'a variety of muses' is the wordplay.
'variety of' indicates an anagram.
'muses' with letters rearranged gives 'ssume'.
'a'+'ssume'='ASSUME'
(Other definitions for assume that I've seen before include "Take for granted or agreed" , "Take for granted, suppose" , "Take on, affect" , "Adopt or take for granted" , "Claim without justification" .)