Eats cold cuts (5)

I believe the answer is:

chews

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'eats' is the definition.
The answer and definition can be both related to consumption as well as being verbs in their -s form.
Maybe there's a link between them I don't understand?

'cold cuts' is the wordplay.
'cold' becomes 'C' (eg on taps).
'cuts' becomes 'hews' (I've seen this in another clue).
'c'+'hews'='CHEWS'

Can you help me to learn more?

(Other definitions for chews that I've seen before include "Masticates" , "Does something with tooth" , "bites" , "toffees" .)

I've seen this clue in The Independent.

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