Crossword Genius

First killer caught for crook (4)

Ross

I believe the answer is:

cane

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

'for crook' is the definition.
(I've seen this in another clue)

'first killer caught' is the wordplay.
I cannot quite understand how this works, but
'first' could be 'a' (first letter of the alphabet) and 'a' is located in the answer.
'caught' could be 'c' (cricket abbreviation) and 'c' is found within the answer.
The remaining letters 'ne' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for cane that I've seen before include "Malacca, perhaps" , "Old school punishment" , "Bamboo or rattan" , "Birch" , "A stick to lean on" .)

I've seen this clue in The Sun.
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