Result of shaving beard off a furry animal (10)

I believe the answer is:

chinchilla

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'furry animal' is the definition.
(I've seen this before)

'result of shaving beard off a' is the wordplay.
'result of shaving beard' becomes 'chinch' (I am not sure about this - if you are sure you should believe this answer much more).
'off' becomes 'ill'.
'chinch'+'ill'+'a'='CHINCHILLA'

Can you help me to learn more?

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

I've seen this clue in The Guardian.

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