My iPad iOS is 10.3.3 and is "current" but the HP LaserJet Pro MFP M29w printer I just bought needs 11 or newer . . . Is there anything I can do to get it to work ?

It probably needs the most recent HP iOS printer app to work or needs a newer version of iOS AirPrint to work, too!

The older version of the HP printer app will probably NOT work with that printer, either.

New AirPrint printers usually want compatibilty with newer mobile devices and OSes.

If iOS 10.3.3 is the highest iOS that iPad can go, you own a over 6-year iPad 4th generation.

The AirPrint printer will not work with an iPad that old with an over two-year old iOS version.

Do you own a computer?

If you have a computer there are third party iOS printing apps, you can install onto your iPad, that will sync, with a installed computer companion app to the iOS printer app, that you need to install on a computer, to print to the iOS printer app, which will transfer this data wirelessly, over your home WiFi network to your computer which cues/queues the printer app on your computer to start up your computer connected printer and then print your iPad data through iPad, to computer, to the wired, connected printer.

You get the idea.

Good Luck to You!