Run the following command to confirm if the Realtek NIC is being detected under the list of installed NICs:
# lspci -v | grep -A1 -i ethernet
You can use the V-Front Online Depot that has the package "net51-drivers".
To install the drivers from the V-Front Online Depot, you must allow ESXi to use Community Supported VIBs.
Run the following command to change the host acceptance level:
# esxcli software acceptance set --level=CommunitySupported
Install the driver for the Realtek NICs:
# esxcli software vib install -n net51-drivers -d https://vibsdepot.v-front.de
When the installation is completed, reboot the host.
The package " net51-drivers" will include the following drivers:
VMware net-r8168, net-r8169, net-sky2 and net-s2io