What do you mean? Why?
(1) Informal norms among the fishermen as to how much fishing you should do. This system is not resilient to immigrants, who don't know the local norms (and may, not unreasonably, feel that the local norms already allot all of the fish to established fishermen), so fishing communities are often fiercely resistant to newcomers.
(2) Legal limits on how much fish you can catch. The idea is that an authority will determine the total quantity of fish to be harvested, and then allot rights to harvest smaller quantities than that piecemeal. Under this system, taking fish without an appropriate license is a crime.
You could move to a system more like our agricultural subsidies (paying people for the pigs they didn't raise), by giving money to anyone who owns a fishing trawler but didn't bring in any fish. But that seems obviously insane compared to the permitting system.
"Informal" cultural norms operate as laws on a small scale, maybe a pre-industrial community and a lake (or grazing commons, like various feudal Europe examples). Any scale that implies depleting oceanic fish is a way to big for this. I would be surprised if any modern era conventions applied to ocean fishing for migrants to have any influence at all.
Cultural norms generally operate on a small group of people. In the modern day, it doesn't take very many people to catch a ridiculous number of fish. So depleting ocean fish is better handled by cultural norms now than it was 500 years ago, when catching a lot of fish meant fielding a lot of boats.
That greatly depends on the type of fish and is not generally true. Many species of fish spend different parts of their lives at different locations. Tuna, salmon and many other pelagic fish travel pretty big distances.
The US government already does something similar for corn. Farmers are paid to not plant it to control market price.