Crossword Genius

One might leave City for this international team (11)

Ross

I believe the answer is:

countryside

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'one might leave city for this' is the definition.
(you might travel from the countryside to a city)

'international team' is the wordplay.
'international' becomes 'country' (I can't justify this - if you can you should believe this answer much more).
'team' becomes 'side' (both can mean a sports team).
'country'+'side'='COUNTRYSIDE'

Can you help me to learn more?

(Other definitions for countryside that I've seen before include "The green and pleasant part of our land" , "Rural areas" , "Rural area" , "Turned so icy (anag.)" .)

I've seen this clue in The Times.
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