Just how big is this imaginary secondary school?
The year 11s will have been at the school 5 years, by that point plenty of teachers will recognise their faces and may have taught their class before. They are certainly going to notice a random child just popping up who looks 5 years younger than the rest of the class.
If you think your child is a genius you have a few options:
You can talk about skipping the child to the year ahead but I think you would have to sufficiently prove that they hadn't missed fundamental knowledge that they need to build on, and the school still might not facilitate this
You can tell the child to work on their behaviour skills as they are apparently not very advanced. Being able to sit and take in information that you personally find boring is actually a very valuable life skills. No one who works wants to sit through yet another CBT on GDPR or information security yet many have to, so its actually a relevant thing to learn. You can then provide external coaching in subjects they want to stretch themselves in outside of school, there are free resources as well as paid ones.
You can home school
You can change schools to one with a more academically challenging environment, if your child really is a child genius then private schools may be able to over scholarships or bursaries to cover the cost of some or most of the fees
If the child really is that clever and really does exist