"In your hand, take this key. So long as you have the makings, then through this simple act of taking...its wielder you shall one day be. And you will find me, friend—no ocean will contain you then. No more borders around, or below, or above, so long as you champion the ones you love."
User inherits what the original guardian possessed; all their experiences, knowledge, abilities, powers, skills, and other features including possibly appearance, with each new generation becoming stronger through the achievements and progress of their predecessors.
The title of Promethea (Promethea) is passed on between hosts of the ancient immaterial spirit Promethea.
The Avatar (Avatar series) is reincarnated between nations, acting as the peacekeeper of the world and being the only person who can bend all four elements...
...Korra being the current Avatar.
Buffy Summers (Buffy the Vampire Slayer) is the Slayer...
... whose death will turn one among many Potential Slayers into the official Slayer...
... until Willow Rosenberg changes the metaphysical law allowing all Potentials to become Slayers.
The Author (Once Upon a Time) is a title given to select individuals by the Sorcerer to record the events of the Enchanted Forest, given a magical-pen to accomplish this, but also have the power to influence the events however they see fit.
Terra (Kingdom Hearts) chooses Riku to succeed him as a Keyblade wielder.
Geomancers (Valiant Entertainment) are an ancestral tribe of aboriginal mystics who commune with and safeguard the world from various threats. Each time one who carries the title of Geomancer dies a new person in the world steps in to take their place.
After the death of Ariel, Kain (Legacy of Kain) was born specifically to take her place as the Balance Guardian of the Circle of Nine.Guardians of Balance could draw upon their fellow members' abilities,or build up their own,to destroy other Guardians should they go astray.
Link (Legend of Zelda series)
After the death of Sara, Seira (Mermaid Melody Pichi Pichi Pitch) was born to take her place as the Mermaid Princess of the Indian Ocean.
Mane Six (My Little Pony: Friendship is Magic) inherit the Elements of Harmony and take their place as Equestria's saviors and eventual rulers.
Young Six (My Little Pony: Friendship is Magic)
The powers of the Maidens (RWBY) pass upon the death of the current holder. That power is then transfered to another young woman, usually the last person that the previous Maiden holds in her thoughts.
The current Four Constellations (Kung Fu Panda: The Paws of Destiny)
Kion (The Lion Guard) discovers that he possesses the Roar of the Elders, a gift bestowed to those destined to lead the Lion Guard.