Priest oversaw church parade (6)
I believe the answer is:
prance
'parade' is the definition.
(parade can mean to prance around)
'priest oversaw church' is the wordplay.
'priest' becomes 'p' (ecclesiastical abbreviation).
'oversaw' becomes 'ran' (I've seen this in another clue).
'church' becomes 'CE' (abbreviation for Church of England).
'p'+'ran'+'ce'='PRANCE'
(Other definitions for prance that I've seen before include "Move with high springy steps" , "Of horse, raise forelegs and spring" , "Frolic" , "Leap or skip" , "Caper, swagger" .)