Can I use an alternative license on GitHub that isn't listed? Specifically I want to use License Zero.
I must admit that the phrasing of the question is a bit unclear, at least to me. I am assuming you meant something in the spirit of "Can I use a license that isn't listed on choosealicense.com, and thus isn't recognized by GitHub, when I host my project there?"
If my understanding of the question is correct, the answer would be a resounding yes. As the creator of the project, you can use whatever license you wish to license your project, or even write a new one yourself (although, if you're not a lawyer, that's probably an ill-advised idea). Just place the license in a
LICENSE.txt file, and you're good to go.
The worst thing that will happen is that GitHub wouldn't "magically" recognize the license, and you won't get some of its bells and whistles around it, like explanatory text, or the ability to search according to it.
Note that you can also request GitHub to add a license, although License Zero doesn't seem to listed in one of appropriate sources GitHub would consider, so you may need to do some extra work beforehand (e.g., get it listed by the OSI).