Part of greater honesty that's starting to be seen between Swiss banks (5)
I believe the answer is:
rhone
'that's starting to be seen between swiss banks' is the definition.
(river which starts in Switzerland)
'part of greater honesty' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'RHONE' can be found hidden inside 'greater honesty'.
(Other definitions for rhone that I've seen before include "River rising in Switzerland and flowing into the Mediterranean" , "French river from Alps to Mediterranean" , "River at Avignon and Arles" , "River at Lyons" , "River running through France to the Med" .)