Hello,
Unfortunately, Apple removed drivers for ASIX chipset from macOS, so now you have manually install drivers and then you have to enable this driver in the Security&Privacy tab.
But for example, this adapter is plug&play:
i-tec USB 3.0 Metal GLAN Adapter (Ethernet / Lan, 6.10cm)
It uses Realtek chipset and drivers are part of macOS.
Best regards
i-tec Team