0) Use Nexerelin and Industrial Evolution mods
1) Capture or liberate Kapteyn Starworks, size 4, Isirah Star System
2) Capture or liberate Kanta's Den, size 3, Magec Star System
3) *untested* Capture from pirates or make your own colonies with an upgraded heavy industries and a privateer base (ikr, it's like you're almost a pirate yourself at this point)
3.1) Keep good diplomatic profile to ensure positive relationships with other factions, you don't want to raid them.
3.2) Enjoy your colonists raiding pirates by themself lol
4) Continue to scan the map and capturing/abandoning/liberating any core pirate colonies
4.1) Continue to search and destroy any outside of core pirate stations that threatening your colonies (or if they just have a bounty)
5) Make some powerful Special Task Groups to outsource p.4 from you, as well as simple patrol HQs to automatically defend your own worlds
5.1) Also use "Request a fleet" option to make base strikes or even invasions
You can't rid of pirates completely. It's really an idea, you'll basically need to kill an every single humanoid in order to achieve your victory. But you can make their life as miserable as possible, apply the same or even bigger pressure, denying their opportunities, destroying their hopes, dreams, and lives. Do that, and you will be praised by the redacted civilized part of the sector forever.
*by liberating I mean transferring the market to Independent since they don't appear on a victory condition score tracker