can I use my 21.5 inch imac late 2009 model as a "target display" for my new macbook air?

You can use that model iMac as a display with certain other Macs, but a new MacBook Air is not one of them.

Refer to Use your iMac as a display with target display mode - Apple Support.

It's no substitute for TDM but you can use Screen Sharing: Share the screen of another Mac - Apple Support.

Sorry, but neither of those Mac models support Target Display Mode.

Please carefully read all of the system and model requirements for Target Display Mode,

at > Use your iMac as a display with target display mode - Apple Support

+2, Nope Target Display Mode never worked on 21.5" 2009 iMacs and the MBA is too new. If you need an external display for the MBA, please buy one. Overall a much more reliable, easy to setup and not expensive solution than Target Display Mode ever was.

No.

In 2009 only the 27-inch iMacs supported TDM. And, as John wisely points out, no Mac newer than 2019 or running higher than macSO 10.15 Catalina can take advantage of Target display mode.

In 2009 only the 27-inch iMacs supported TDM.

Thanks for the reminder!