Carbonara hastily served up depresses North African, maybe (7)

I believe the answer is:

saharan

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'up depresses north african maybe' is the definition.
I can't tell whether this defines the answer.

'carbonara hastily' is the wordplay.
'SAHARAN' is hidden back-to-front in amongst the letters.
However, I am not sure how the hidden word is indicated.

'served' acts as a link.

Can you help me to learn more?

(Other definitions for saharan that I've seen before include "Relating to the North African desert" , "Baking" , "Deserter" .)

I've seen this clue in The Irish Times.

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