Insist on staying with the rubbish due for collection (6,2,2)

I believe the answer is:

refuse to go

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'insist on staying' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'with the rubbish due for collection' is the wordplay.
'with' means one lot of letters go next to another.
'the rubbish' becomes 'refuse' (both can mean waste material).
'due for collection' becomes 'togo' (I am not sure about this - if you are sure you should believe this answer much more).
'refuse' next to 'togo' is 'REFUSE TO GO'.

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