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Bahraini travelling around east, having rejected an area in Ireland once (8)

Ross

I believe the answer is:

hibernia

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'bahraini' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

I don't understand the remainder of the clue.

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(Other definitions for hibernia that I've seen before include "Latin name for Ireland" , "Old or poetic name for Ireland (8)." , "land once" , "Ancient Ireland" , "Poetic name for Ireland, now archaic" .)

I've seen this clue in The Times.
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