The Caribbean of 1720 is home to many dozens of ports belonging to the three great powers: Britain, France, and Spain. Each port is a valuable source of goods, equipment, and mission patrons. Players use PvE missions to destabilize a port, making it eligible for conquest by their nation. With enough players doing enough missions, the conquest mode begins and the ocean for many leagues around the port becomes an open PvP environment. This unlocks new PvE missions to smuggle in supplies, destroy fortifications, and tilt the odds in your favor. Scheduled PvP battles culminate in a final conflict to either save the port or conquer it.
Every day, each nation receives victory points on the basis of its port holdings. The first nation to reach the goal is declared the victor, and celebrations and awards ensue. Then treaties are signed, ports revert to their original sides, and a new round of conflict begins.
If by this statement you classify Pirates of the Burning Sea as a "PvP game".... I'll pass. Aside from that, I've heard the PvP is consensual.