Religious leader beginning to talk the talk! (6)

I believe the answer is:

rabbit

'the talk' is the definition.
(rabbit can informally mean to talk)

'religious leader beginning to talk' is the wordplay.
'religious leader' becomes 'rabbi' (Jewish religious leader).
'beginning to' says to take the initial letters.
The first letter of 'talk' is 't'.
'rabbi'+'t'='RABBIT'

(Other definitions for rabbit that I've seen before include "Bunny; chatter idly" , "Fur; chatter (colloq.)" , "Fast-breeding hopper" , "Roger, Peter or Brer" , "Bit bar (anag.)" .)

I've seen this clue in The Independent.

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