There are three primary methods to update Realtek Ethernet drivers, ranked from easiest to most advanced.

If you built the PC or the manufacturer site is outdated, you can use the Realtek downloads page.

Fixes core stability bugs responsible for sudden "Default Gateway Not Available" errors.

For the most generic, latest versions, you can visit Realtek's official download center.

This is the fastest, safest approach utilizing Microsoft's certified driver repository.

Programs like Driver Booster or Snappy Driver Installer can automatically find and update all outdated drivers. They are convenient but often contain adware, may try to charge for features, or could install the wrong driver. from official sources, and always create a system restore point first.

[Start Menu] -> [Device Manager] -> [Network Adapters] -> [Right-Click Realtek] -> [Update Driver]