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Cat that’s trapped a rook’s airway (6)

Ross

I believe the answer is:

larynx

I'm a little stuck... Click here to teach me more about this clue!

'airway' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'cat that's trapped a rook's' is the wordplay.
'cat' becomes 'lynx' (lynx is a kind of cat).
'that's trapped' indicates putting letters inside.
'rook' becomes 'r' (abbreviation in chess).
'a'+'r'='ar'
'lynx' going around 'ar' is 'LARYNX'.

Can you help me to learn more?

(Other definitions for larynx that I've seen before include "Air passage" , "Site of the vocal cords" , "Where growls come from" , "Source of squeaks" , "part of throat with vocal chords" .)

I've seen this clue in The Sunday Times.
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