Finishes off impromptu stories, some indeed not new (4)
I believe the answer is:
used
'not new' is the definition.
(I've seen this before)
'finishes off impromptu stories some indeed' is the wordplay.
'finishes off' indicates one should take the final letters (take the finishing letters off of the words).
The last letters of 'impromptu stories some indeed' are 'USED'.
(Other definitions for used that I've seen before include "Accustomed, having been put into service" , "Exploited group" , "Employed - exploited" , "no stranger" , "with some traffic" .)