Once considered to be a safe haven by any English or French pirates who wished to strike at Spanish interests, this has changed much over the past forty years. Starting with the appointment of Lieutenant Governor Henry Morgan in 1675, once a privateer of some repute himself, the port has been working to improve its reputation. The town began to rely more and more on being both a convenient midway point for slave ships heading to the New World and for slaves being brought to the Jamaican sugar plantations, anti-piracy laws were passed in 1687 to dissuade pirates from using the town as a port of call. The Earthquake of 1692 caused a fair amount of damage, but the still stood strong, though it was used as a convenient opportunity to purge many of the seedier elements within the city.
Now, with an even more strict crackdown on piracy, led by Governor Nicholas Laws and the newly-promoted Commodore George Henderson, arrests, imprisonments, and executions have all increased, with all notable pirates that used to call the port home, leaving before they too are captured or killed.
NOTE: Going with the idea that the Earthquake of 1692 did happen, but was nowhere near as devastating, so Port Royal is still the major trading capital of Jamaica, though it is regularly rocked by hurricanes