The most common and most likely answer to this crossword clue is the 4 plus 3 plus 2 plus 3 plus 4 letter word COME OUT IN THE WASH
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "Become apparent/as the Witham, Welland, Nene and Great Ouse do" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case become apparent/as the witham, welland, nene and great ouse do = come out in the wash.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.