http://www.nzpam.govt.nz/cms/permits/minerals/types
New Zealand Petroleum & Minerals issues permits to prospect, explore and mine minerals.
These permits are defined in the Crown Minerals Act 1991 and the Minerals Programme for Minerals 2013.
Minerals permits are classified as Tier 1 or Tier 2 - read more about the different classifications.
Permits do not give the permit holder automatic rights to access the permit area. Generally for exploration and mining activities, permit holders must arrange land access with the landowner and occupier. For minimum impact activity, 10 days' notice is required (except over special classes of land, such as urban conservation land)
Prospecting permits:
Prospecting permits give the permit holder the right to prospect for specified minerals. Allowed activities are very low-impact, such as literature searches, geological mapping, hand sampling, offshore sampling (by low-impact mechanical methods), or aerial surveys.
Generally onshore permits are no larger than 500 square kilometres, and offshore permits have a maximum area of 5,000 square kilometres. Permits are normally granted for two years. An extension for up to half the permit area can be granted for two years and this can be extended up to a total of four years from the permit commencement date.
Permits are granted to the first acceptable work programme. They are normally exclusive (unless a non-exclusive permit is requested).
Try having a look at this link ghost it will be a good place to start but I don't think it will help you with dredging... good luck on the adventure