In the original GTA games (I don't play GTA Online), if you did a lot of illegal activities in public, you'd get pursued by the police. Death or staying out of trouble was all that could help you.
This could be implemented in Sea of Thieves as the "Royal Navy" where you gain infamy with the more players that you kill and ships that you sink. If your infamy gets high enough, the Navy sends a single ship after you. Then if you kill it or keep killing others, they send a fleet and then an armada.
Not only would this help PVE players, because PVP players would have to worry about the Navy, but it would be a good challenge for PVP experts having to fight off a fleet of skilled NPC ships all at once. And then if a group of PVP ships got together, they could even take on the armada.
The infamy would have to stick with you even when you log off. It only goes away over time (if you don't do anything bad) or by helping out other players (giving chests, helping with raids, etc.).
I believe this could be a good compromise between the PVP and PVE crowds since the PVE crowds would gain protection and the PVP crowds could gain a new enemy. It could even serve as new content where you are tasked with taking on or helping out the Navy.
Thoughts?
