Gone off a place in Italy (5)

I believe the answer is:

genoa

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'in italy' is the definition.
('Genoa' is part of 'italy')

'gone off a' is the wordplay.
'off' indicates an anagram.
'gone' with letters rearranged gives 'geno'.
'geno'+'a'='GENOA'

'place' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for genoa that I've seen before include "Type of rich fruit cake" , "North Italian port" , "Seaport in northwestern Italy" , "Italian city has no age, oddly" , "City of Italy" .)

I've seen this clue in The Mirror.

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