How do I turn on OverPower Level?

Solution 1:

You must be level 72 (or level 80 if Commander Lilith & the Fight for Sanctuary is installed) when you finish the Digistruct Peak gauntlet (the mission A/More History of Simulated Violence) to unlock Overpower Level 1.

Upon reaching level 72 or 80 (depending on whether Digistruct Peak is the only DLC installed or not) and the completion of the Digistruct Peak arena in Ultimate Vault Hunter Mode, Overpower Level 1 unlocks. To access the additional Overpower levels, players must exit the game and reload. Upon restarting the game, a prompt appears that will offer options which Overpower level is desired.

Every time players play through the Digistruct arena at the highest available level, they will unlock the next Overpower level. There are 10 Overpower levels in total with both DLC, meaning the arena must be completed at least 10 times in order to reach the maximum level at Overpower level 10.

With the release of the DLC "Commander Lilith & the Fight for Sanctuary" the Overpower levels have been increased to 10.

^{Source: Borderlands Wiki, "Ultimate Vault Hunter Upgrade Pack Two: Digistruct Peak Challenge - Overpower Levels" article}

Solution 2:

Once you have earned an Overpower level, you will need to exit back to the Main Menu to activate it. As long as you have chosen the character who has unlocked the Overpower level(s), and have chosen to play in Ultimate Vault Hunter Mode, when you hit Continue, a prompt will come up asking you how many Overpower levels you want to enable.