I Mac compatibility to Canon printer TR4720

Also, the Canon TR4720 is an AirPrint model.

About AirPrint - Apple Support

https://mfi.apple.com/account/airprint-search

Even an OS X 10.9 Mavericks computer should support basic AirPrint printing (without additional drivers/software), provided that the printer and the Mac computer are connected to the same network (Wi-Fi router).

https://www.canon-europe.com/support/consumer_products/apple_airprint_guide/

So, you could perhaps carry out an experiment with AirPrint before upgrading. It may work.

The 2010 iMac support High Sierra 10.13

How to download and install macOS - Apple Support

There is a long list of macOS drivers for that printer.

https://www.usa.canon.com/support/p/pixma-tr4720?

The Mid 2010 iMac is capable of running macOS 10.13.6 (High Sierra). What I don't know is what version of macOS is required to download the Canon printer driver for this particular printer.