Trickle from river (from mouth) (4)

I believe the answer is:

ooze

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'trickle' is the definition.
(I've seen this in another clue)

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

(Other definitions for ooze that I've seen before include "River-bed mud; leak slowly" , "... sweat" , "Mud at bottom of river" , "Seep out slowly" , "Trickle slowly out, like mud" .)

I've seen this clue in The Sunday Times.

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