The most common and most likely answer to this crossword clue is the 5 letter word RHONE
I've seen this crossword clue in The Guardian
R
H
O
N
E
More clues leading to the result RHONE
- With new start, shone in river
- Some clear honey a flower in Europe supplied
- River, extremely rough one
- Odd heron in French river
- Royal Highness associated with a certain river
- River or bay — or at least sound
- Hard right backed by a certain French department
- Wine region right to improve
- Nothing gets one out of a river for another
- Part of greater honesty that’s starting to be seen between Swiss banks
Buddy explains!

The straight part
We know that "that’s starting to be seen between Swiss banks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s starting to be seen between swiss banks = rhone.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.