Its mouth may be full of fish (5)

I believe the answer is:

river

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

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for river that I've seen before include "Flowing water" , "Exe, Po" , "Current" , "course of 1d [ADVENTURE]" , "Large flow of liquid" .)

I've seen this clue in the Evening Standard.

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