Crossword Genius

Successive letters daughter’s left for hotel’s cook (4)

Ross

I believe the answer is:

chef

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'cook' is the definition.
(both can mean someone who cooks)

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for chef that I've seen before include "Key kitchen worker" , "Kitchen head" , "Professional cook" , "member of kitchen staff" , "one in the restaurant" .)

I've seen this clue in The Times.
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