Hill-climbers link flag with policewoman (4,3,4)

I believe the answer is:

jack and jill

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'hill-climbers link' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'flag with policewoman' is the wordplay.
'flag' becomes 'jack' (jack is a kind of flag).
'with' becomes 'and'.
'policewoman' becomes 'jill' (I can't justify this - if you can you should believe this answer much more).
'jack'+'and'+'jill'='JACK AND JILL'

Can you help me to learn more?

(Another definition for jack and jill that I've seen is " Hill-climbers, water-fetchers and fallers?".)

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

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