Perhaps Snape, now given to Harry, has some sort of knowledge or power that Dumbledore wants Harry to access. So, Harry might try to extract that information from Snape. Snape, being his usual self, could be resistant at first but gradually realizes that he has to cooperate with Harry for the greater good, like fighting against the remaining Death Eaters or uncovering some dark magic secrets.
One possible plot development could be that Harry initially struggles with having Snape under his 'command' in some way. Since they had a very strained relationship in the original series, Harry might be hesitant to trust Snape even if Dumbledore has given him this new role. He could start by trying to figure out Snape's true intentions.
One possible plot development could be that Dumbledore gives Snape to Harry as a sort of guide in the wizarding world. Snape, with all his knowledge and experience, could show Harry things that Dumbledore couldn't. This might include some dark arts knowledge that could be used against Voldemort. It could also be a test for both of them. For Snape, to see if he can truly be selfless in helping Harry, and for Harry, to learn to trust Snape despite their past differences.
Another possibility is that the main antagonist could be some sort of ancient evil that is awakened by the events in the fanfic. Dumbledore might have given Snape to Harry because he sensed this new threat. This ancient evil could have powers that are unknown to the modern wizarding world and it would be up to Harry and Snape to figure out how to defeat it.
It could be a very complex relationship. Harry has always had a deep - seated hatred for Snape due to Snape's treatment of him in the past. But with Dumbledore's action, Harry might be forced to see Snape in a new light. At first, it could be full of suspicion and wariness on Harry's part.
Perhaps Dumbledore is being forced in this fanfiction. There could be some dark magic or powerful dark wizard threatening Hogwarts or the wizarding world. Dumbledore, in a desperate attempt to save everyone else, gives Harry to Voldemort as a sacrifice. But Harry, being the hero he is, could find a way to turn the situation around and defeat Voldemort from within his lair.
Maybe the story could develop with Snape trying to understand why Harry is a Malfoy fan. He could start to investigate Harry's past interactions with the Malfoys and any hidden reasons behind his admiration.
Perhaps Snape is under a spell or a magical obligation that makes him carry Harry in such an unusual way. This could lead to comical situations at first, with Harry being confused and Snape being grumpy about it. But then, they might find themselves in a magical location where they have to rely on each other. Snape's knowledge of magic and Harry's natural courage could combine to solve a mystery or defeat a foe. For example, they could be trapped in an ancient, enchanted forest, and by working together, they find a way out and also uncover a hidden power or artifact.
One possible plot development could be that Naruto becomes extremely powerful and is able to defeat enemies with ease. The new bloodlines might give him unique abilities like enhanced speed, strength, and elemental control. He could also face challenges as others might fear his newfound power.
Well, it could be that Dumbledore steals Harry's Invisibility Cloak for some 'greater good' he believes in. Maybe he thinks it's too dangerous for Harry to have at a certain point in time.
One possible plot development could be that Snape initially struggles with his feelings towards Harry. He has his own past grudges against James Potter, but as he sees the extent of Harry's abuse, his protective instincts kick in. He might start teaching Harry advanced magic in secret, away from the prying eyes of the other Hogwarts staff and students, especially those who might be skeptical of Snape's motives.
In this fanfiction, it could also be that Harry's Gryffindor nature starts to rub off on Snape in some ways. They might have arguments about how things should be done, but through these interactions, Snape might start to see the value in Harry's way of thinking. And Harry, on the other hand, might learn some of Snape's more cautious and calculating ways, which could help him in his future battles.