Revealed that one was in debt, on the quiet (6)
I believe the answer is:
showed
'revealed' is the definition.
('show' can be a synonym of 'reveal')
'one was in debt on the quiet' is the wordplay.
'one was in debt' becomes 'owed' ('they owed' means 'they were in debt').
'on' is a charade indicator (letters next to each other).
'the quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'owed' after 'sh' is 'SHOWED'.
'that' is the link.
(Other definitions for showed that I've seen before include "presented" , "Demonstrated or displayed" , "Demonstrated or depicted" .)