The most common and most likely answer to this crossword clue is the 3 letter word EMS
I've seen this crossword clue in The Times
E
M
S
Buddy explains!

The straight part
We know that "river" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case river = ems.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EMS mean?
EMS noun- The name of the Latin-script letter M.
- A unit of measurement equal to the height of the type in use.