A dash for the river (4)

I believe the answer is:

arun

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'the river' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'a dash' is the wordplay.
'dash' becomes 'run' (I've seen this in another clue).
'a'+'run'='ARUN'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for arun that I've seen before include "River of West Sussex" , "W. Sussex district, river" .)

I've seen this clue in the Evening Standard.

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