Crossword Genius

Have a drink up in Italian city (4)

Ross

I believe the answer is:

pisa

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'italian city' is the definition.
(city in Italy)

'have a drink up' is the wordplay.
'have' becomes 'a' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a drink' becomes 'sip' (I've seen this before).
'up' is a reversal indicator (in down clue: letters go upwards).
'a'+'sip'='asip'
'asip' back-to-front is 'PISA'.

'in' is the link.

Can you help me to learn more?

(Other definitions for pisa that I've seen before include "City on the River Arno" , "much-visited city" , "Site of the famous leaning tower" , "Location of leaning tower" , "Italian city with famous tower" .)

I've seen this clue in The Irish News.
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