To sleep rough in rubbish? Not right! (4)
I believe the answer is:
doss
'to sleep rough' is the definition.
(I've seen this before)
'rubbish? not right' is the wordplay.
'rubbish?' becomes 'dross' (I've seen this before).
'not' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'dross' with 'r' taken out is 'DOSS'.
'in' is the link.
(Other definitions for doss that I've seen before include "Sleep in rough or improvised accommodation" , "go to bed" , "Sleep in a makeshift bed" , "going off to sleep" , "Sleep like a tramp" .)