Noisy animal yet a wily one (3)

I believe the answer is:

fox

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'a wily one' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.

'noisy animal' is the wordplay.
'noisy' becomes 'f' ().
'animal' becomes 'ox' (castrated bull).
'f'+'ox'='FOX'

'yet' acts as a link.

Can you help me to learn more?

(Other definitions for fox that I've seen before include "Deceive; Reynard" , "Baffle; mammal" , "Animal; to cheat" , "earth-dweller" , "Vulpine creature" .)

I've seen this clue in the Evening Standard.

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