Animal gets cold in the Far East (10)

I believe the answer is:

chinchilla

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'animal' is the definition.
(chinchilla is a kind of animal)

'cold in the far east' is the wordplay.
'cold' becomes 'chill' (chill can mean cold).
'in the' indicates putting letters inside.
'far east' becomes 'china' (I can't explain this - if you can you should give a lot more credence to this answer).
'chill' going within 'china' is 'CHINCHILLA'.

'gets' is the link.

Can you help me to learn more?

(Other definitions for chinchilla that I've seen before include "little furry animal" , "Rabbit" , "furry creature" , "Soft grey fur" , "(Fur of) a small South American rodent" .)

I've seen this clue in The Irish News.

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