Muse as priest organised errand (11)
I believe the answer is:
terpsichore
'muse' is the definition.
(I know that Terpsichore is a muse)
'priest organised errand' is the wordplay.
'organised' is an anagram indicator.
'errand' becomes 'chore' (I've seen this in another clue).
'priest' is an anagram of 'terpsi'.
'terpsi'+'chore'='TERPSICHORE'
'as' acts as a link.
(Other definitions for terpsichore that I've seen before include "this muse being the inspiration?" , "I inspire dancers" , "Inspiring female" , "The Muse of dance" .)