Another possibility is that he showed an ability related to his Nine - Tails chakra in a more controlled way. He might have raised his hand to demonstrate that he could access a certain amount of the Nine - Tails' power without losing control. This could have been a new form of power - up for him, where he could use the Nine - Tails' strength to enhance his physical abilities like speed, strength, and endurance while still maintaining his own consciousness.
Perhaps he showed an enhanced sensory ability. In the Chunin Exam, being able to sense opponents better can be a great advantage. Naruto might have raised his hand to volunteer for a task that required this ability, and it was a sign that he had improved his sensing skills to a new level. He could detect even the faintest chakra signatures and movements of his opponents, which would have surprised everyone.
Maybe he saw an opportunity to help his friends. If there was a task or a challenge in the Chunin Exam that required someone to step forward, Naruto, being the selfless person he is, raised his hand to protect or assist his comrades. For example, if there was a dangerous opponent that his friends were having trouble with, he would volunteer without hesitation.
Perhaps Naruto raises his hand to answer a really tough question in the written part of the Chunin Exam. He could use some of his unique experiences or the wisdom he's gained from his friends to come up with an unexpected but brilliant answer. This would surprise the examiners and his fellow candidates, and might earn him some respect from those who used to look down on him.
Naruto may become more confident. By raising his hand, he's taking initiative, which is a sign of growing self - assurance. He's no longer waiting for others to pick him or tell him what to do.
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.
Naruto would likely become more self - reliant. As a ronin, he doesn't have the support of a village. So during the Chunin Exam, he has to trust his own instincts and skills more. He may also become more cautious as he realizes he can't always count on backup.
He might face disappointment from his friends and mentors. His friends who were also participating in the exam might feel let down, and his mentors, like Kakashi, could be concerned about his decision and how it will affect his future as a ninja.
The plot could involve a mysterious figure who uses a singing jutsu during the Chunin Exam. This jutsu affects the minds of the participants, causing them to act out of character. Naruto, with his strong will, is able to resist it to some extent. He then teams up with some of the other genin to figure out who is behind the jutsu and stop it. Along the way, they all have to sing in order to counter the effects of the jutsu, leading to some comical and heartwarming moments.
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.
It could be due to a physical or mental injury. If Naruto got seriously injured during the Chunin Exam, and he didn't think he could recover in time to compete effectively, he might give up. Mentally, if he was somehow affected by a genjutsu that made him lose his confidence or will to fight, that could also lead to his decision to give up.
He could have the ability to see chakra flow in extreme detail. This would allow him to not only detect enemies from afar but also predict their moves based on how their chakra is moving. He could also potentially have enhanced vision in non - combat situations, like being able to see in the dark much better.