Trashy literature is sensitive matter (4)
I believe the answer is:
pulp
This clue is a double definition.
'trashy literature' is the first definition.
'sensitive matter' is the second definition.
'is' is the link.
(Other definitions for pulp that I've seen before include "Soft plant tissue" , "Mush" , "Soft, soggy mass" , "Cheap fiction" , "Crush" .)