Priest set out mission with article about dancing (13)
I believe the answer is:
terpsichorean
'about dancing' is the definition.
'priest set out mission with article' is the wordplay.
'set out' indicates an anagram.
'mission with' becomes 'chore' (I can't explain this - if you can you should believe this answer much more).
'article' becomes 'an' (indefinite article).
'priest' anagrammed gives 'terpsi'.
'terpsi'+'chore'+'an'='TERPSICHOREAN'
Can you help me to learn more?
(Other definitions for terpsichorean that I've seen before include "Relating to dancing" , "of dance numbers" , "become a dancer" , "Related to dancing - chain store rep (anag)" .)