The latest Mac driver from an OEM website doesn't ensure it is compatible with the version of macOS that you have omitted here. Can you open that PDF in Apple's Preview or Adobe's Acrobat Reader application? That's to confirm it is not damaged.
Your C4570 is supported natively in macOS without any vendor drivers by Apple's built-in AirPrint when it is networked. Other than the Ethernet cable, or Wi-Fi (if capable), there should be no other data cables connected to it.
With the device powered, visit the System Preferences/ System Settings : Printers & Scanners panel. If the C4570 appears under Printers, right-click on it and choose Reset Print System… This will remove the device from the Printers listing, and now you want to add it back which will present a new panel with a bonjour detected entry for your Printer. Click that, and the Use: selector should automatically configure for AirPrint, though it may not explicitly show AirPrint as the driver choice. Then click Add. Right-click on the new entry under Printers and choose Default Printer.
Here is what that process looks like with my networked Samsung laser:
