Joins up again to stagger about North Island streets (9)

I believe the answer is:

reenlists

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'joins up again' is the definition.
I can't tell whether this definition defines the answer.

'stagger about north island streets' is the wordplay.
'stagger' becomes 'reel' (both can mean to move around without balance).
'about' indicates putting letters inside.
'north' becomes 'N' (abbreviation).
'island streets' becomes 'ists' (I can't explain this - if you can you should believe this answer much more).
'reel' going around 'n' is 'reenl'.
'reenl'+'ists'='REENLISTS'

'to' acts as a link.

Can you help me to learn more?

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

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