You can summon a Noble to any Keep belonging to a family that you either have neutral or better Rapport with or are in the same Alliance as you.
  • Tap on their city
  • Tap "Keep" to view their Keep
  • Tap on your ''Family'' button
  • Pick the Noble(s) you wish to bring over and tap "Summon"
Once they arrive you can have them interact with others or drag them to a room to help boost it. Idle Nobles in foreign Keeps hang out in the Foyer.

Your rapport with the other player is important here. Having bad rapport won't allow you to summon anyone in their keep or even view their keep.