Old paper breaks secret gently (6)
I believe the answer is:
softly
'gently' is the definition.
(synonyms)
'old paper breaks secret' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'paper' becomes 'FT' (Financial Times newspaper).
'breaks' is an insertion indicator.
'secret' becomes 'sly' (I've seen this in other clues).
'o'+'ft'='oft'
'oft' going into 'sly' is 'SOFTLY'.
(Other definitions for softly that I've seen before include "With a quiet and gentle voice" , "In a quiet way" , "Lightly, quietly" , "Piano" , "Quietly or gently" .)