One possibility is that Naruto, while running away with this Itachi - related element in the fanfiction, is trying to protect it from those who would misuse it. He might be on a solo mission to keep something Itachi left behind safe, and in the process, he discovers new aspects of his own power and purpose. For example, if it's a special jutsu or a piece of knowledge, Naruto could experiment with it in his own unique way, leading to new and unexpected developments in his abilities.
Well, Naruto might run away with Itachi's ideals or some memento of Itachi. Maybe he uses it to become stronger and face new enemies. He could also be on a journey to uncover more secrets about Itachi that no one else knows.
In the fanfiction, Naruto running away with something related to Itachi could be a catalyst for a major shift in the ninja world. It could lead to a split among the villages as some might see Naruto's actions as either heroic or a threat. He may be pursued by various groups, both good and bad. Along the way, Naruto could encounter old friends who are now conflicted about whether to support him or not. This situation would force Naruto to re - evaluate his relationships and his place in the world, all while being in possession of this important Itachi - related item or concept.