A priest, old-fashioned, got around, moved with the times (7)
I believe the answer is:
adapted
'moved with the times' is the definition.
'a priest old-fashioned got around' is the wordplay.
'priest' becomes 'p' (ecclesiastical abbreviation).
'old fashioned' becomes 'dated' (I've seen this before).
'got around' means one lot of letters goes inside another.
'p' put into 'dated' is 'dapted'.
'a'+'dapted'='ADAPTED'
(Other definitions for adapted that I've seen before include "Made suitable for new purpose" , "Changed to suit anoter purpose" , "accommodated" , "Became adjusted" , "Altered" .)