You can keep bees in Palmerston North urban areas. Hive placement is important. Locate your hives so they don't become a nuisance or danger to other residents. The Animals and Bees Bylaw sets out the conditions you need to meet to keep bees in the urban area, including the maximum number of hives you can have.
All beekeepers must register their hives with the Management Agency, National Foulbrood Pest Management Plan
If you want to sell your honey, you will have to comply with the Food Act 2014. See the Ministry for Primary Industries website for food safety rules for low-risk businesses