Busy old English prior (7)
I believe the answer is:
engaged
'busy' is the definition.
(similar in meaning)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for engaged that I've seen before include "Promised - book - fighting" , "as a result of a proposal" , "Spoken for" , "Fully committed - to get married?" , "Plighted; hired" .)