The story could develop in many ways. Harry might use his connection to death to access the spirit world in the Avatar universe more easily than others. This could lead to him discovering secrets about the origin of bending or the history of the Avatar. He could also use his Gryffindor courage to stand up against any form of oppression in the Avatar world. His skills in magic, combined with his new - found knowledge of the Avatar world, could make him a powerful force for good or, if misused, a great danger. As he interacts with the different nations and characters, he'd slowly change the dynamics of the Avatar world, all while dealing with his own identity as the master of death.
He could start by using his skills to survive the harsh environment. His ability to cheat death might mean he can take more risks while exploring Skyrim's dangerous dungeons. For example, he might be able to brave the traps and monsters without as much fear of dying.
He would likely cause a stir. His magic is different from the Dragon Age magic. He could potentially use the Elder Wand to defeat powerful foes with ease. Maybe he'd teach some of his spells to the mages there.
In fanfiction, Harry as the Master of Death could also start a new school of magic in the Marvel universe. This could attract both mutants and regular humans with an aptitude for magic. It would be a place where they could learn about the different aspects of magic, especially those related to life and death. This would not only expand the magical community in the Marvel universe but also create a new generation of heroes and magic - users who have a different understanding of death and its implications.
Well, it could be that Harry Potter, as the Master of Death, arrives in Asgard. He might use his unique magical abilities to interact with the Asgardian magic system. Maybe he'd help Asgard in some sort of crisis, like fending off a new and powerful enemy. His knowledge of the Deathly Hallows could give him an edge in dealing with threats that are even beyond what the Asgardians are used to.
Harry Potter himself could be a potential Avatar of Death. Given his connection to Voldemort and all the death and sacrifice he has witnessed, he might develop some sort of connection to death in a more profound way. It would be a very dark and different take on his character, but it could also add a whole new layer of depth.
Harry would likely become more fearless. Knowing that Death is his guardian, he'd have a sense of security that most others don't. He might take more risks in his battles against the dark forces, like confronting Death Eaters without hesitation.
Magic. Harry Potter, as the Master of Death, would bring his powerful magic to the RWBY world. His spells could be a new form of combat or defense against the Grimm. For example, the Stunning Spell could be used to immobilize Grimm, giving the RWBY characters an advantage in battle.
Well, it could be that Harry has complete control over death. He might be able to bring back the dead, or at least communicate with them freely. Maybe he uses this power to right the wrongs of the wizarding world, like resurrecting those who died unjustly during the war. He could also use it to gain ultimate knowledge, as death is often associated with hidden secrets in the wizarding lore.
His character would develop by learning from the different bending styles. For example, waterbending's fluidity could teach him new ways to move and fight. He'd also grow through his interactions with the Avatar and the various tribes. Maybe he'd start to see the value of balance in a new light, not just in power but also in nature and society. Naruto might even develop a new form of jutsu inspired by bending.
One possibility could be that Harry uses his mastery of death to communicate with the spirits in the Avatar world, similar to how he could interact with the dead in the Potterverse. He might gain new powers related to the elements, as his connection to death gives him a deeper understanding of the balance in nature, which is crucial in the Avatar world.