Broadly speaking, that’s the role of Rogue Traders.
They’re essentially very wealthy Imperial Citizens with a permit to explore unexplored regions, with a view to finding worlds suitable for colonisation.
Typically, they’re though of as adventuring beyond the nominal rim of the Galaxy, but given the sheer size of the Galaxy, and how sparse the Imperium actually is, that’s not necessarily true.
From there? It really, genuinely depends. Some worlds might be little more than Iron Age or worse. Some might be more medieval in society. Others yet may hold levels of technology baffling to the Adeptus Mechanicus.
Their fleets are often fairly autonomous, but will contain different elements of The Imperium, such as Ecclesiarchal elements and Ad Mech elements. And if they don’t, it’s generally true that they’ll summon allies via Astropathic Communication.
So, hypothetically (but not necessarily) any element of The Imperium would do much the same.
Powerful as a Battlebarge and it’s attendant fleet is (assuming they’ve all washed up on the same shore), much the same would happen. Typically, Astartes are above the politics of The Imperium, because that’s not their role in the grand machine.
I suspect all Chapters would send an Astropathic message of some kind - either to an allied Forgeworkd, Recruitment World or Rogue Trader,, then largely be on their way, because wherever they were going still needs them. They may even simply report back to their home world or home fleet.
But, if there’s a clear and present Xenos or Heretical threat, they’d most likely engage it and give it a damned good shoeing- because that absolutely is their role. But that will all depend upon the size of the threat. Little point stirring up a Hornet’s best you can’t feasibly confront, not if you can summon/redirect other elements to do the job, before heading back off to where you were meant to be going
Automatically Appended Next Post: But, as is my favourite answer?
It Depends.
Let’s say that whatever mishap has ultimately stranded the Astartes wherever they’ve wound up, also means that they can’t simply get back to business?
Then they’ll look to take more direct action to bring it into the fold. And that method will depend on the system, the Chapter and Fleet elements present.
If it’s a Feral World, with no sign of genetic deviation? Chances are it’ll be claimed as a Chapter Recruitment World.
If it’s more advanced? Depends on their hostility.
The important sources here are the early Heresy Novels. Not that the later ones are crap, because they’re not. Just that the early one’s best show The Great Crusade and how compliance was achieved.
Some planets, having been cut off from the rest of humanity for millennia, welcomed their brothers with open arms, and welcomed compliance. Others needed some form of persuasion. Some required a good kicking. And others still were wiped out to a man because they were irrevocable in their current form.