Relative in southeast river stroll (7)

I believe the answer is:

saunter

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'stroll' is the definition.
(I know that stroll can be written as saunter)

I don't understand the remainder of the clue.

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(Other definitions for saunter that I've seen before include "Relaxed stroll" , "Walk casually or jauntily" , "'Amble, stroll (7)'" , "Leisurely stroll" , "Walk in a slow and relaxed manner" .)

I've seen this clue in The Sun and The Times.

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