On a broader scale, Naruto's achievement as a Chunin could affect the relationships between the Hidden Leaf and other ninja villages. Other villages might view the Hidden Leaf as even more powerful or might be more cautious in their interactions with it. His new rank could also open up opportunities for diplomatic missions or alliances that weren't possible before.
One possible plot could be Naruto facing unique challenges during the Chunin Exams that are different from the canon. Maybe he has to deal with a new type of opponent, like a ninja from a far - off land with strange and powerful jutsu. This would test his skills and growth as a ninja in new ways.
He faces tougher opponents. In the Chunin Exams, the competitors are more skilled. Naruto has to deal with more complex jutsus and battle strategies from his rivals. Also, he has to prove his leadership skills, which is crucial for a Chunin.
The plot could involve Naruto passing on his unique skills and values to the new generation of ninjas. He might teach them about the importance of teamwork, just like how he learned with his own team. For example, he could share his experiences in the Chunin Exams and how they shaped him as a ninja.
One possibility is that he gains enhanced speed and stealth. As a chunin, he'd need to be more covert in his missions. He could learn to move so quietly that even sensors would have a hard time detecting him. And his speed could be on a level where he can quickly close the gap between him and his enemies without them realizing it until it's too late.
His relationship with Sasuke might become more competitive. Since they are both aiming for higher levels of ninja skills, they would constantly push each other. With Sakura, Naruto might be more respected as he has achieved the Chunin rank, and she could see him in a new light.
His relationship with Sasuke could become more competitive yet respectful. They'd both see each other as equals in a new way. Sasuke might start to see Naruto as a real rival worthy of his attention, and Naruto would be more confident in their interactions.
Maybe he realizes the exam is too dangerous or he discovers some unfairness in it. In the original Naruto story, Naruto has faced many difficulties and moral dilemmas during the Chunin Exam. So in the fanfiction, similar situations might push him to quit.
Naruto's teaching style would likely be very hands - on. He's not one to just stand and lecture. He'd probably jump right in and demonstrate techniques himself. For instance, if teaching a new jutsu, he'd do it multiple times until the students got it.