You could write a fanfiction where a group of students accidentally open the Chamber again, but this time they have to work together to close it before it causes real harm. They could face different challenges than Harry did, like dealing with new types of magical creatures that were also trapped in there. It would be interesting to see how different characters from different houses interact and use their unique skills to solve the problem.
One idea could be exploring the backstory of the Chamber more deeply. Maybe look into how Salazar Slytherin really built it and what his true intentions were beyond just getting rid of Muggle - borns. Another could be a story where a new student discovers a hidden passage within the Chamber that leads to an even greater mystery. For example, they might find an ancient spellbook that has the power to change the very fabric of Hogwarts.
A cool fanfiction idea would be to set the story in modern times, many years after the events in the Chamber of Secrets. A new generation of students discovers that there are still remnants of the dark magic from the Chamber lurking in Hogwarts. They then embark on a journey to fully cleanse the school of this dark influence, using both old and new magic they've learned at Hogwarts.