No. Maxon lists ZBrush for Windows, macOS and iPad only. There is no Linux version, and the licence you hold does not include one.
ZBrush by Maxon · Design, CAD & 3D · No way to run it
ZBrush is the standard digital sculpting program and it has never been released for Linux. Maxon's product
page names Windows, including Windows on ARM, macOS with Apple Silicon support, and iPadOS, and notes that
a licence covers desktop and iPad together. Linux does not appear.
Blender is the replacement most sculptors move to, and it is free. Its sculpting mode handles dynamic
topology, masking and brushes, and for character and creature work people do produce finished results with
it. It is not as smooth as ZBrush at very high polygon counts, and features such as ZRemesher and the ZBrush
brush library have no exact equal, so expect the work to feel different rather than identical.
One habit carries over. A graphics tablet is central to sculpting, and most common tablets are recognised by
Linux without you installing anything. It is still worth plugging yours in and testing pressure sensitivity
before you commit to the switch.
Your .ztl files cannot be opened on Linux. Before the Windows machine goes, export your sculpts as OBJ or
FBX, and export your high detail as normal or displacement maps, because those carry the surface detail
across when the raw mesh would be too heavy to work with.
Only relevant if what you liked was painting textures and concepts rather than sculpting. Excellent tablet support and free.
Your files: No ZBrush file support. Works with ordinary image files for texture painting.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need ZBrush. Everything else you do can move.