A Red ‘1’ notification will appear on your Coliseum table when an Era unit you own can be Leveled Up.

Simply enter the Colisuem, tap Battle, and the unit that can level up will have a red dot notification. Tap and hold on the character to enter the Level Up menu. 

Note: Loaned Units are automatically leveled up after collecting Loaned Unit Era level tokens. They cannot be manually leveled up.