APT is the Advanced Package Tool for Debian (or Debian-based distros). On Arch for example, you’d use pacman, on SUSE, zypper, on RedHat you use RPM and so on and so on.
On Clear Linux, there does not seem to be any package manager, just the possiblity to install packages via flatpak or compile it from source. I don’t think there’s a Pantheon-flatpak, and compiling it from source on Clear Linux seems not to be easy or wise to do, at least I don’t think it is.
So if you want to use Pantheon, I guess using elementaryOS, Ubuntu or Debian would be the easiest way; another would be, for example, installing Arch Linux (or, if you want it easier, EndeavourOS) and install pantheon on top of it via pacman.