Upgrading NixOS so that it uses a different channel is simple.
When you run following command as root:
You should see a list of channels. If you did not touch channels so far, you should see this:
By running the following command (as root):
nix-channel --add https://nixos.org/channels/<channel version> nixos
you will remove the 21.05 channel and replace it with <channel version>.
To apply the change, you need to run following command:
nixos-rebuild switch --upgrade
which is going to rebuild your system with your current configuration and updated packages from the channel you switched to.