They dishearten the rabbits, the beasts! (4)
I believe the answer is:
rats
'beasts' is the definition.
(rat is a kind of beast)
'they dishearten the rabbits' is the wordplay.
'they' becomes 'ra' (I can't explain this - if you can you should give a lot more credence to this answer).
'dishearten' suggests removing the centre.
'the rabbits' becomes 'talks' (rabbit can mean to talk).
'talks' with its middle taken out is 'ts'.
'ra'+'ts'='RATS'
'the' is the link.
Can you help me to learn more?
(Other definitions for rats that I've seen before include "Mild oath - sewer residents" , "deserters" , "Heels" , "(Hunts) rodents - expression of irritation" , "Rodent pests" .)