Crossword Genius

Do a stretch up the river (5)

Ross

I believe the answer is:

reach

I'm a little stuck... Click here to teach me more about this clue!

'do a stretch' is the definition.
'reach' can be an answer for 'do' (thesaurus). I am not certain of the 'a stretch' bit.

'up the river' is the wordplay.
I cannot quite understand how this works, but
'up' could be 'each' (I've seen this in another clue) and 'each' is present in the answer.
'river' could be 'r' (abbreviation for river) and 'r' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for reach that I've seen before include "Extend an arm" , "Be received" , "It's an advantage for a boxer" , "Put out the hand for a part of the river" , "Get to < throw up in the old" .)

I've seen this clue in the Evening Standard.
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