Copy what used to be your secret (8)
I believe the answer is:
stealthy
'secret' is the definition.
(thesaurus)
'copy what used to be your' is the wordplay.
'copy' becomes 'steal'.
'what used to be your' becomes 'thy' ('thy' historically meant 'your').
'steal'+'thy'='STEALTHY'
(Other definitions for stealthy that I've seen before include "Acting in furtive or covert manner" , "Done in a quiet or secretive way" , "Underhand" , "Unobtrusive" , "Acting in quiet or secret way" .)