Obviously, you cannot simply get rid of shark finning as a practice (like any other culturally rooted practice). Limiting the number of sharks you can fish at a certain time will allow shark population to remain more stable, protecting the environment as well as preventing a market crash due to lack of resources required to produce shark fin soup.
Shark-finning is the wasteful practice of catching sharks, taking their fins, and then tossing them back into the ocean where they die. This threatens shark populations, and damages the environment.
Some activists want to ban shark fin soup to try to stop this practice. However, it is considered a delicacy and this will just create an underground trade. Instead let's license the sale of shark fins while banning "shark finning". Require every person selling shark fins to have a document proving that they kept the whole shark. Before being allowed to sell the shark fins require them to submit the entire shark caught for inspection.
We could also limit the number given out to conserve populations if banning "shark finning" turns out not to be enough.
Those who are selling shark fins that come from shark farms, enclosed and separated from public waterways could be given the license without limitation and without requiring the whole shark to be used. But they should still be required to somehow prove that the shark fins they sell originated at their farm and not in the ocean. Having the entire shark would seem to me to be the most effective way of doing so, but if there are other ways then that could be allowed, since only using the fins doesn't cause the same sort of ecological damage if it occurs on a farm.