Animal with no tail for religious leader (5)
I believe the answer is:
rabbi
'for religious leader' is the definition.
(Jewish religious leader)
'animal with no tail' is the wordplay.
'animal' becomes 'rabbit' (I've seen this before).
'with no tail' means to remove the last letter.
'rabbit' with its final letter taken away is 'RABBI'.
(Other definitions for rabbi that I've seen before include "Jewish law expounder" , "A Jewish priest" , "legal scholar" , "Hebrew teacher" , "Religious leader of Jewish congregation" .)