Bits of paper from behind the back of shelf (4)
I believe the answer is:
bumf
'bits of paper' is the definition.
(bumf can mean printed material)
'behind the back of shelf' is the wordplay.
'behind' becomes 'bum' (synonyms).
'the back of' says to take the final letters.
The final letter of 'shelf' is 'f'.
'bum'+'f'='BUMF'
'from' is the link.
(Other definitions for bumf that I've seen before include "Useless printed documents" , "Junk-mail" , "official papers?" , "Boring documents etc" , "Printed material" .)