Keep out of sight and dodge bill (6,6)

I believe the answer is:

escape notice

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'keep out' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.

'sight and dodge bill' is the wordplay.
'sight' becomes 'notice' (noticing is a kind of sighting).
'and' means one lot of letters go next to another.
'dodge bill' becomes 'escape' (I can't justify this - if you can you should believe this answer much more).
'notice' after 'escape' is 'ESCAPE NOTICE'.

'of' is the link.

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I've seen this clue in The Guardian.

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