Religious leader not finishing talk (5)
I believe the answer is:
rabbi
'religious leader' is the definition.
(Jewish religious leader)
'not finishing talk' is the wordplay.
'not finishing' means to remove the last letter.
'talk' becomes 'rabbit' (rabbit can informally mean to talk).
'rabbit' with its last letter removed is 'RABBI'.
(Other definitions for rabbi that I've seen before include "Jewish religious teacher" , "A Jewish priest" , "Teacher of Jewish law" , "Religious scholar" , "Hebrew scholar" .)