Heroes can level up only if they gain experience through all the training levels. After the training has been completed, go to [Manage Heroes > Level up] and use the selected amount of "Honors" to level up.
Once a hero levels up, its rank is increased by 1.
From Rank 1 - 3, when the heroes level up, they will stay within the same class but level up to a random hero appearance a rank level higher. From Rank 4 to Rank 6, the hired hero's class can change as well and they can become a completely different class than they were before.