Darling perhaps of chauffeur who'd lost his head (5)

I believe the answer is:

river

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'darling perhaps' is the definition.
(I know that Darling River is a river)

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for river that I've seen before include "Eg, Thames or Nile" , "Large natural stream of water" , "Eg, Amazon" , "Tees, perhaps" , "Natural flow of water" .)

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

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