I see this from time to time. What activities do you propose? Just ideas,
In general, pretty much the same variety that is available normally. Just two conditions:
1. slight rewrite C&P system to lawful / lawless standing. If you do missions for a faction that belong to a power/gov you get "lawful" positive standing AND "lawless" negative standing. The better the standing, the more missions you can get. Per analogy, the lower the standing, the less missions you get. So if you want to work for an anarchy you need to drop your "lawful" standing first so the "lawless" start to like you.
In return you get to build your lawless rep with anarchy factions. Some are more liberal and welcome gray CMDRs, other require some more rep. Progress system. The more you progress into "lawless" the more you are a target of "lawful".
2. distinct lawful/lawless sector separation. GalMap should have new filter - law status. Government ruled systems should be countered with lawless. Police interventions only in lawful, bounty hunting in lawless.
This way, if enough "lawless' standng you could have same delivery/supply missions, just within anarchy systems. Mining requests as well. In fact - whole spectrum of missions, just limited to lawless factions.
In the end we could have cargo convoys routes, for both lawful and lawless, cargo raids, mining resources from other side fields... whatever you dream. Sadly entire bubble and colonia is a mere mix of systems without any real impact whether it is democracy, kingdom or anarchy. Every system treats me alike.