Crossword Genius

Thing to do before one can swallow carbon cut (4)

Ross

I believe the answer is:

chew

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'thing to do before one can swallow' is the definition.
I can't tell whether this defines the answer.

'carbon cut' is the wordplay.
'carbon' becomes 'C' (C is the chemical symbol for carbon).
'cut' becomes 'hew' (hew can mean to chop or cut).
'c'+'hew'='CHEW'

Can you help me to learn more?

(Other definitions for chew that I've seen before include "Prepare to swallow" , "work with canines" , "Bite repeatedly" , "Try to eat" , "Gnaw" .)

I've seen this clue in The Irish Times.
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