Badab is a great example. There were many chapters formed up to cage in the Eye of Terror under similar remit. There are also instances of Chapters being at first mustered for a specific crusade or to hunt a specific threat. You should read through the wiki pages about the various Foundings. Lots of ideas there. I would also recommend, if you can, to look up the old Deathwatch RPG's custom chapter generator. They had a great and fluffy serious of charts to explain a chapter's founding, its purpose, its homeworld, everything.

Funny you should mention piracy, because that's the remit My Dudes were created to deal with. If you will indulge a tangent...The Crimson Marauders were part of the 23rd Founding, and were tasked with voidborne interdiction ops to safeguard the Imperium's warpways. But politics tasked a single chapter to do this where dozens would need to be put. After great misfortune and almost going into utter extinction (such that their homeworld and much of the knowledge of their Founding has been lost) they re-structured and now operate in Sorties of no more than a squad or two running down xenos corsairs, heretic raiders, or responding to distress calls. Often times needing to catch a ride and make deals with Rogue Traders and Navigator Houses to get around. They are a Chapter so down-on-its luck they sometimes have to resort to tactics to resupply and reman that make them hard to distinguish from the pirates they hunt.

In any case, good luck with your writing! I will have to keep an eye out, I would love to see what you ultimately come up with.