Double-dealing gets around trading place quickly (7)
I believe the answer is:
smartly
'quickly' is the definition.
(thesaurus)
'double-dealing gets around trading place' is the wordplay.
'double-dealing' becomes 'sly'.
'gets around' indicates putting letters inside.
'trading place' becomes 'mart'.
'sly' going around 'mart' is 'SMARTLY'.
(Other definitions for smartly that I've seen before include "wasting no time" , "pronto" , "at a brisk pace" , "How the chic are turned out" .)