Crossword Genius

Only small parts of the course of a river (4)

Ross

I believe the answer is:

tees

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

'river' is the definition.
(River Tees)

'only small parts of the course of a' is the wordplay.
I cannot quite see how this works, but
'small' could be 's' (abbreviation - e.g. clothes size) and 's' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
'course' could be 'e' and 'e' is present in the answer.
A single letter 'e' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for tees that I've seen before include "banker" , "English river" , "Golf pegs" , "used by golfers" , "Stockton's river" .)

I've seen this clue in the Evening Standard.
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