Can't find hailo pcie class

We first need to make sure you can see the Hailo-8 when running lspci. Without that we do not need to worry about the driver.

I suspect the issue is your Thunderbolt adapter. Can you please tell me the exact model, tell me how much is costs and provide a link to where you bought it so I can have a look? If the adapter or cable does not support PCIe it will not work.
Please read the following post with some more information about this.

How can I connect a Hailo-8-8l to my pc or laptop

Alternatively you can also try to plug-in the module into your motherboard directly or via a PCIe card adapter. See the same post above.