Clean piece over here that has a tendency to collect dirt (4,4)

I believe the answer is:

dust trap

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'here that has a tendency to collect dirt' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'clean piece over' is the wordplay.
'clean' becomes 'dust' (dust can mean to clean up dust).
'piece' becomes 'part' (synonyms).
'over' shows that the letters should be reversed in order.
'part' reversed gives 'trap'.
'dust'+'trap'='DUST TRAP'

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I've seen this clue in The Irish Times.

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