Type of restaurant, the oldest of which still operating today was founded in Naples in 1738 (8)

I believe the answer is:

pizzeria

(Other definitions for pizzeria that I've seen before include "Italian-style restaurant" , "Shop making and selling popular Italian food" , "Type of Italian restaurant" , "Kind of Italian restaurant" , "Shop that makes popular Italian fare" .)

I've seen this clue in The Independent.

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