Sleep interrupted by rook is rubbish (5)
I believe the answer is:
dross
'rubbish' is the definition.
(I've seen this before)
'sleep interrupted by rook' is the wordplay.
'sleep' becomes 'doss' (I've seen this before).
'interrupted by' indicates putting letters inside.
'rook' becomes 'R' (chess abbreviation).
'doss' placed around 'r' is 'DROSS'.
'is' is the link.
(Other definitions for dross that I've seen before include "Scum on molten metals" , "Something of inferior quality" , "Waste matter, refuse" , "Worthless stuff" , "of no value" .)