Is there a visa which covers...

[osmyth]

...working in NZ for an overseas company.

Think this may be a long shot but is there a visa (work or residency) which would cover the following:
working/living, ideally permanently, in NZ
for a UK company, not an NZ one
UK company doesn't have a presence in NZ
would be employee or sole trader (contractor)
not a secondment or for a short period of time or for a particular event

Is basically the option of remote working for a UK (overseas) company whilst residing in NZ.

Thanks very much.

[JandM]

You couldn't get a visa on the basis of this situation, no. The NZ government issues a visa to a foreigner as a kind of swap - s/he brings her/his skills to be employed and pay tax in the NZ job market, and in return, receives permission to live and work in NZ.

If you had already obtained residence and were living in NZ, and THEN a foreign company offered you that kind of opportunity, you would be entitled to do it, but you would have to have qualified in some other way first.