He’s to buzz around old priest (6)
I believe the answer is:
helium
'he's' is the definition.
(synonyms)
'buzz around old priest' is the wordplay.
'buzz' becomes 'hum' (synonyms).
'around' means one lot of letters goes inside another.
'old priest' becomes 'eli' (Biblical character).
'hum' going around 'eli' is 'HELIUM'.
'to' is the link.
(Other definitions for helium that I've seen before include "Light colourless gas used in balloons" , "Light colourless gas used in airships" , "Lightest noble gas" , "Balloon-filling element" , "... ditto: symbol He" .)