Actor’s part offering no new stories (4)
I believe the answer is:
lies
'stories' is the definition.
(to tell stories can mean to lie)
'actor's part offering no new' is the wordplay.
'actor's part' becomes 'lines' (lines learned by an actor).
'offering no' indicates named letters should be taken away.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'lines' with 'n' removed is 'LIES'.
(Other definitions for lies that I've seen before include "Tall stories" , "pork pies" , "Assumes a horizontal position" , "Falsehood" , "Untruths" .)