Animal finally going for synagogue official (5)
I believe the answer is:
rabbi
'synagogue official' is the definition.
(rabbis are Jewish religious teachers)
'animal finally going' is the wordplay.
'animal' becomes 'rabbit' (I've seen this before).
'finally going' means to remove the last letter (the final letter is removed).
'rabbit' with its final letter taken off is 'RABBI'.
'for' acts as a link.
(Other definitions for rabbi that I've seen before include "Blue" , "Jewish law expounder" , "legal scholar" , "Religious leader of Jewish congregation" , "Jewish minister" .)