Keep exclusively clean rubbish! (7)
I believe the answer is:
hogwash
'rubbish' is the definition.
(I have seen 'Utter rubbish ' mean 'hogwash' so perhaps 'rubbish' could also mean 'hogwash')
'keep exclusively clean' is the wordplay.
'keep exclusively' becomes 'hog' (as in hogging something from others).
'clean' becomes 'wash' (washing is a kind of cleaning).
'hog'+'wash'='HOGWASH'
(Other definitions for hogwash that I've seen before include "Pigswill - nonsense!" , "Colloquial nonsense to pig cleanser" , "bull" , "Baloney" , "Pig food" .)