New Zealand has fisheries management with a lot of quota provided to Maori Iwi (tribes) who in turn might sell the quota or run a fishing business outright or in partnership. Additionally Maori have customary fishing rights for funerals and other customary events.
I am not quite sure what you mean by property rights and what it means in reference to other places.
On a side note, New Zealand just changed a number of significant fishing rules for commercial and recreational fisherman. The new restrictions on types of fishing that are allowed are to help protect both the Hectors dolphin (est. 10,000 left) and the Maui dolphin (est. 50 left.
It is good to see these unilateral efforts are possible in NZ due to their being no competing interests who have legal entitlement to the same waters.
Annecdotally, It is still relatively easy to go to the beach in NZ and catch a few fish of 2 - 6kg in size.
https://www.mpi.govt.nz/protection-and-response/sustainable-...