Endless anger in cheap newspaper (3)
I believe the answer is:
rag
'cheap newspaper' is the definition.
(rag can mean a low-quality newspaper)
'endless anger' is the wordplay.
'endless' means to remove the last letter.
'anger' becomes 'rage' (rage is a kind of anger).
'rage' with its final letter taken away is 'RAG'.
'in' acts as a link.
(Other definitions for rag that I've seen before include "Disreputable newspaper" , "Bit of material" , "Torn cloth or despised newspaper" , "Disreputable paper" , "Fun week for college students" .)