Eccentric priest displays wit and liveliness (6)
I believe the answer is:
esprit
'liveliness' is the definition.
(I know that esprit is a type of liveliness)
'eccentric priest' is the wordplay.
'eccentric' indicates an anagram.
'priest' with letters rearranged gives 'ESPRIT'.
'displays wit and' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for esprit that I've seen before include "Vivaciousness" , "Lively wit" , "Vivacity, liveliness" , "Liveliness of wit" , "Sprightliness" .)