One standard solution to overfishing offered by economists is to essentially privatize the sea by creating individualized transferable quotas (ITQs) that give individuals and firms an incentive to fish at a sustainable level. Where intellectually coherent, the approach can be criticized on a number of grounds.
This Grist post does a good job of doing so. It points out the importance and difficulty of setting an appropriate Total Allowable Catch (TAC), the enormous problem of subsidized overcapacity, as well as bycatch and social justice issues.
ITQs may well be part of a sustainable global fisheries regime, especially where it comes to well-studied coastal fisheries off the shore of a single state with a strong regulatory capacity. When it comes to dealing with the pillage of the open ocean, however, they don’t really stand a chance.