This is NOT about player to player piracy. This is intended as a system to a) add a resource and money sink for the game, and 2) give a little PvE flair to already existing mechanics.
Piracy in this sense would be represented by fleets of unaligned, NPC controlled ships. They would move from system to system, targeting a planet and causing “environmental” effects until either paid, pacified, or bored. These effects would be things like reducing base efficacy, destroying planetary infrastructure, lowering happiness and depopulating. Governments would have the ability to pass a motion paying the pirates for protection, in return for which the pirates would leave that planet alone and move on. Governments would also be able to disable or reduce the productivity of infrastructure, in return for taking less damage, as well as issuing letter of marque to players to have them attack the pirates.
This system would also add a selection of weapons players can equip ships with (yes molp, you can finally have your railguns and PDCs 
) The type, size, and capabilities of said weapons would be determined by the size of the cargo bay aboard the ship. Once commissioned into service, a military ship would lose the ability to transport goods. Instead, it could be sent into orbit of a planet under pirate blockade and attempt to break said blockade. While any player with a gunship could accomplish this, governments would be able to use a contracting system (similar to gateways) to pay a player to deal with the incursion. This adds a financial incentive to players becoming effectively mercenaries. Multiple players would also be able to band together to deal more damage to the pirates.
Pirates would form from unemployed, unhappy pops. Each tier would have a multiplier, inversely proportional to tier, that determines how quickly it created pirates. A sixth “pirate” tier of pops would be added. Pops that are unemployed and have happiness below 50% would have a chance of becoming pirates. Planets well below 50% may have employed pops defecting as well, as would planets with excessive unemployment. This incentivizes planetary governors to maintain a happiness above 50%, while also not having too much unemployment.
Pirates on planet would have a slight happiness and productivity penalty. They might also begin to cause similar troubles to a fleet if they grow too large. A government motion to “raise militias” could be enacted to purge large quantities of pirates, at the expense of a week’s population growth. These purges might also be extendable to unemployed pops, as a drastic measure to prevent pirates.
If a planet has more pirates than regular pops, it becomes a pirate enclave. Any bases on planet are removed, the government is disbanded and the treasury sacked, and while many pops will attempt to flee, some will become pirates as well, furthering the problem. In time these enclaves can also spawn the roving fleets outlined above, causing further havoc. After a period of time these enclaves would dissolve into squabbling, and would likely disband. A more immediate solution would be a planetary invasion by players. Ships fitted with proper modules would be able to destroy pirate pops, restore order and allow the planet to be recolonized.