Crossword Genius

A caterer all right but the company comes first (4)

Ross

I believe the answer is:

cook

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

'a caterer all' is the definition.
I can't judge whether this definition defines the answer.

'right but the company comes first' is the wordplay.
'right but' becomes 'ok' (both are affirmative answers. I am not sure about the 'but' bit.).
'the company' becomes 'co' (abbreviation).
'comes first' is a charade indicator (letters next to each other).
'ok' after 'co' is 'COOK'.

Can you help me to learn more?

(Other definitions for cook that I've seen before include "Heat food" , "Brown?" , "Kitchen worker" , "Doctor" , "Falsify - chef" .)

I've seen this clue in The Irish News.
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