I think it is clear on the NZ medical council website that you must work in an approved house officer position (this is a first year house officer position = intern) for one year.
http://www.mcnz.org.nz/get-registere...zrex-clinical/ (see almost the bottom of the page).
You should note that you cannot become registered with the medical council in NZ without a job.
You used to be able to apply directly to the DHBs or via some localised clearing systems but I don't know how ACE is working/going to work. You seem to have missed the deadline for this year for ACE though (and probably will have a fairly low priority based on their published criteria), so might be better off applying to some of the accredited (for intern - I think it is most of them anyway) DHBs to see if they still have places.