Maybe the older brother was separated from Harry when they were young. He could have been kidnapped by Death Eaters who thought he had some special power. Years later, he returns, having been trained in dark magic but still having a good heart deep down. He has to struggle with the dark influence while also trying to reconnect with Harry and their family at Hogwarts.
One possible plotline could be that the older brother is a prodigy at magic and overshadows Harry in the beginning. For example, he might be the top of his class in every subject at Hogwarts. This could create some jealousy or a sense of inadequacy in Harry at first. But as the story progresses, they could learn to support each other and the older brother could use his skills to help Harry in his battles against Voldemort.
The older brother could be a Squib in this fanfiction. While Harry is a famous wizard, his older brother has to deal with the disappointment of not having magic. This could lead to a story of the older brother finding his own way in the non - magical world but still being an important part of Harry's life, perhaps giving him advice from a different perspective on how to handle the Muggle - wizard relations.