Secretary off again to arid tableland (9)

I believe the answer is:

patagonia

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'arid tableland' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.

'secretary off again to' is the wordplay.
'secretary' becomes 'PA' (abbreviation for personal assistant).
'off' indicates anagramming the letters.
'again'+'to'='againto'
'againto' with letters rearranged gives 'tagonia'.
'pa'+'tagonia'='PATAGONIA'

Can you help me to learn more?

(Other definitions for patagonia that I've seen before include "far-off land" , "part of South America" , "Southernmost region of S America" , "Region of South America" , "Craggy region" .)

I've seen this clue in The Telegraph.

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