Assuming you are running a Home Assistant OS install bare metal on the NUC, request support be added for your NIC here:
Until then (or if this applies Ethernet adapter Motorcomm YT6801 Gigabit Ethernet Adapter support in HAOS · Issue #3387 · home-assistant/operating-system · GitHub ) you can run HA in a VM. e.g. install Proxmox and add the NIC driver (if not supported natively). Then install HAOS, Installing Home Assistant OS using Proxmox 8