Slate rubbish about central part of case (5)
I believe the answer is:
roast
'slate' is the definition.
(I've seen this before)
'rubbish about central part of case' is the wordplay.
'rubbish' becomes 'rot' (both can mean nonsense).
'about' is an insertion indicator.
'central part of' means to look at the middle letters.
The central letters of 'case' are 'as'.
'rot' going around 'as' is 'ROAST'.
(Other definitions for roast that I've seen before include "Sunday dinner" , "Cook with dry heat" , "Cook, eg, joint of meat" , "Cooked joint" , "cooked a certain way" .)