Next, one is shown list of meat and fish courses in Italian restaurant (7)

I believe the answer is:

secondi

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'shown list of meat and fish courses in italian restaurant' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'next one' is the wordplay.
'next' becomes 'second' (I am not sure about this - if you are sure you should believe this answer much more).
'one' becomes 'i' (Roman numeral).
'second'+'i'='SECONDI'

'is' acts as a link.

Can you help me to learn more?

(Other definitions for secondi that I've seen before include "Parts of duet" , "Bass parts" , "Lower parts" .)

I've seen this clue in The Irish Times.

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