can't upgrade my mac

High Sierra 10.13.6 is the highest possible upgrade for a mid 2011 iMac.

Also see the following from Identify your iMac model - Apple Support

iMac (21.5-inch, Mid 2011)

Model Identifier: iMac12,1

Part Number: MC309xx/A, MC812xx/A

Newest compatible operating system: macOS High Sierra

You may be able to use a recent model printer via AirPrint without installing any software that came with the printer. I haven't tested that but may be worth a try if you already have the printer. Print wirelessly from your Mac to your printer - Apple Support

Hi,

Any information about the printer make and model?

See also a discussion about macOS 10.13 High Sierra and an HP printer.

What is the latest OS I can upgrade to if… - Apple Community