Maintains oversight on prisons and betting shops (5,4)

I believe the answer is:

keeps tabs

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'prisons and betting shops' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.

'maintains oversight' is the wordplay.
'maintains' becomes 'keeps' ('keep' can be a synonym of 'maintain').
'oversight' becomes 'tabs' (I can't explain this - if you can you should give a lot more credence to this answer).
'keeps'+'tabs'='KEEPS TABS'

'on' acts as a link.

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I've seen this clue in the Sydney Morning Herald.

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