You can fight in raids and dungeons to get more experience for your heroes. But it is a hard way especially when your heroes has reached high levels. As the alternative method, you can increase a hero level, using tomes of experience. For this sake, you should tap on the Altar structure and choose the Tactics Academy option. Then you need to select a hero you want to upgrade. Tap on books you have to get experience points (the Earn EXP tab). Then push on the Earn EXP button.
Every 20 levels you should spend additional resources (money, Flames, and Honor Badges) to upgrade a hero star level. If you won't do this, you will not be available to increase next levels of your hero.