In the neighbourhood restaurant - the ultimate secret (6)

I believe the answer is:

closet

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'secret' is the definition.
('closet' can be a synonym of 'secret')

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for closet that I've seen before include "Cupboard (to come out of)" , "A small room - best to come out of it" , "Covert" , "Small room or wardrobe" , "A small room - secret?" .)

I've seen this clue in the Irish Times.

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