Goes from estuary to source, by the sound of things, from this Levantine city (6)

I believe the answer is:

beirut

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'city' is the definition.
(Beirut is an example)

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

(Other definitions for beirut that I've seen before include "Capital city of Lebanon" , "Middle East capital" , "Lebanon's capital" , "Lebanese capital" , "Capital of 21 across" .)

I've seen this clue in The Irish Times.

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