Country fair Jack missed in song (7)

I believe the answer is:

austria

'country' is the definition.
(Austria is an example)

I don't understand how the remainder of the clue works.

(Other definitions for austria that I've seen before include "EU country" , "USA art I send to European state" , "Central European republic" , "US tiara to be found in this country, oddly" , "Central European country" .)

I've seen this clue in The Guardian.

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