New priest’s liveliness of wit (6)
I believe the answer is:
esprit
'liveliness of wit' is the definition.
(I've seen this before)
'new priest's' is the wordplay.
'new' indicates anagramming the letters.
'priest' anagrammed gives 'ESPRIT'.
(Other definitions for esprit that I've seen before include "Sparkling quality" , "Group morale is . . . . . . de corps" , "Vivaciousness" , "wit from France" , "What good corps needs" .)