On the positive side, new and better policies could be implemented. If the old council was corrupt or stagnant, getting rid of them would open the door for fresh ideas and reforms. Naruto could bring in new people with different perspectives to help run the village, leading to a more prosperous and fair Konoha.
He might use his influence as a hero. Naruto has a lot of friends and supporters in the village. By getting them to see his point of view about the council's inefficiencies or wrongdoings, he could start a movement to oust the council. For example, he could talk to his old friends like Shikamaru, who is intelligent and might be able to come up with a strategic plan.
One consequence is a change in his physical strength. Kurama provided Naruto with a huge boost in power, so without it, he might not be as strong in terms of brute force. However, this could also force him to become more strategic in combat.
Snape could face some backlash from the Ministry. If they find out that he was involved in getting rid of Umbridge, they might try to find ways to punish him or at least keep a closer eye on him. However, his skills at subterfuge would likely help him avoid any serious consequences.
Well, in most cases, his friends would likely try to rescue him. Sasuke might put aside his differences for a while and join forces with Sakura and the others. They'd probably start by gathering information about the council's motives and the location where Naruto is being held.
In fanfiction, when Naruto gets called by the council, he might be faced with various challenges. Maybe they will question his loyalty to the village again, despite all he has done. It could also be that they want to assign him a difficult mission that only he can do because of his unique abilities.
He could use his Rasengan. If he manages to gather enough chakra secretly, he can surprise his captors with a powerful Rasengan and break free.
If Naruto gets rid of Kurama in fanfiction, one way it could change the story is that Naruto would lose a major source of his power. He'd have to rely more on his own natural skills and training. This might make him seem more vulnerable at first, but it could also lead to him developing new and unique abilities. For example, he could focus more on his Sage Mode training and become even more proficient in it without Kurama's chakra interfering or overshadowing his progress.
One reason could be betrayal. If the council betrays Naruto in some way, like selling him out to an enemy, he might kill them in retaliation.
It's also possible that Naruto uses his strong willpower. We know Naruto has an unbreakable spirit. He could use that determination to resist the effects of the seal until it eventually breaks. He might enter a state of deep meditation or concentration and focus his chakra in a way that overpowers the seal.
Kakashi could also be of assistance. With his Sharingan, he might be able to analyze the seal and figure out its weak points. Then he could guide Naruto on how to target those weak points and break the seal.