To level up Nobles you either need Noble XP or Family XP.

• Noble XP cannot be tracked as a whole. Each Noble accumulates their own XP as they perform actions. This XP can be spent on increasing your Noble's level and stats through a Noble's profile page. From main page, tap on the "Family" tab then choose a Noble to see their profile. Noble XP can be acquired through specific noble actions like trading, exploring dungeons, commanding armies, etc. 
• Family XP can be tracked as a whole, as it's a consumable resource that can be used for any Noble of your choice. Family XP can be acquired from chests, rewards, and if a Noble's XP bar is full, they will earn Family XP instead of Noble XP.

Keep in mind, that if the action you're performing is related to your Noble's role, then more Noble XP will be awarded!