The most common and most likely answer to this crossword clue is the 4 letter word OUSE
I've seen this crossword clue in The Times
O
U
S
E
More clues leading to the result OUSE
- Report of sludge in one of three rivers
- Report of discharge in river
- Dwelling lacking hot running water
- Insect heading off for a flower perhaps
- English flower in residence leaving hotel
- Removed head of pointless flower
- Valueless river?
- Bird that’s abandoned lake or …
- Local channel showing latter parts of Dynasty
- Apparently futile flower
Buddy explains!
The straight part
We know that "one of three rivers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one of three rivers = ouse.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.