Mediterranean horse elixir (4,7)

I believe the answer is:

mare nostrum

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'mediterranean' is the definition.
(mare nostrum is a kind of mediterranean)

'horse elixir' is the wordplay.
'horse' becomes 'mare' (mare is a kind of horse).
'elixir' becomes 'nostrum' (I can't justify this - if you can you should believe this answer much more).
'mare'+'nostrum'='MARE NOSTRUM'

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I've seen this clue in the Sydney Morning Herald.

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