Estonia's perplexed with old barren state (10)

I believe the answer is:

desolation

'barren state' is the definition.
(state of being barren or desolate)

'estonia's perplexed with old' is the wordplay.
'perplexed with' is an anagram indicator.
'estonia' with its letters anagrammed with 'old' gives 'DESOLATION'.

(Another definition for desolation that I've seen is " Misery, wretchedness".)

I've seen this clue in The Guardian.

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