I think Ben would probably monitor Imperial movements and keep an eye out for any other Jedi or Sith visitor in the hope of protecting Luke.

Something like the comic where Maul turns up at the Lars farm makes sense (just not Maul).
We need to get the impression that Owen doesn’t like Ben and has a good reason for his resentment.

You can imagine him meditating in his house or monitoring communications chatter and discovering some threat or Rebel in distress and getting discretely involved but in a manner that makes Owen worried for Luke’s safety.

Ben is also very nostalgic for the Republic so it might be cool to make the film a bitter sweet film where there is a successful resolution to whatever plot comes his way but it reminds him of the world he has lost.