Cheers stories, but not Independent stories (5)
I believe the answer is:
tales
'stories' is the definition.
(I know this)
'cheers stories but not independent' is the wordplay.
'cheers' becomes 'ta' (both can informally mean thank you).
'stories' becomes 'lies' (to tell stories can mean to lie).
'but not' indicates named letters should be taken away.
'independent' becomes 'i'.
'lies' with 'i' taken out is 'les'.
'ta'+'les'='TALES'
(Other definitions for tales that I've seen before include "Stories, yarns" , "They might be tall" , "provided for defective juries" , "Stale kind of stories" , "Stories, perhaps tall ones" .)