Go to an aa centre or something like that (I got my form from my BHS instructor). You need form DL4.
Fill it in, go back to aa centre or equivalent, you pay $22.20 as an application fee, and they consider it case by case. The application is sent to Christchurch for consideration.
Get your restricted first, it is only under exceptional circumstances that they will give an exemption on a learners license. (probably because you have then passed a practical test, and proved you can ride)
You need to state traffic offenses and the like, and then give details as to what condition you applying for an exemption (ie, mine was the 250cc) on what license (mine was 6R), and what reasons you think you should have an exemption. They will need to see that you will be as safe with the exemption (for me, once I pointed out the details I plainly stated I was less safe without).
My reasons were weight impacting on crap brakes, dangerous suspension (still bottoming out after being stiffened), top heavy = vulnerable in winds, all leading to being dangerous in corners.
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