GitHub does not allow nested repositories (IIRC Git doesn’t allow this for bare repositories).
However, you can use submodules to nest repositories on the “client side” in the working tree.
You need to clone the parent directory.
Then, add the sub-repository as a submodule:
git submodule add https://github.com/username/sub_repo.git
The sub_repo module will then be linked to the parent repo and can be found in the sub_repo directory.
Commit (.gitmodules and sub_repo), push and you’re done.