Prestige level can be raised only for 4 and 5 star birds in the game. You can increase prestige to level 10 by tapping the ‘Bird Team’. Select the bird which’s prestige level you’d like to upgrade and as soon as you’re happy with the result, confirm this action to proceed.

Note that 4 and 5 star birds can no longer be used to level up prestige-level birds, but selling them now gives Prestige Totems, instead of Evolution Materials.