Can I use my old 21.5” iMac as a monitor for my new m1 chip MacBook Air

No. Target Display Mode requires the computer connecting to the iMac to be introduced in 2019 or earlier and be running macOS Catalina or earlier. As this is not the case with your M1 MacBook Air, this will not be possible.

For more information, please see the documentation on Target Display Mode here.

I misspoke. The answer is definitely no, you cannot use Target Display Mode with a new Mac:

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

We need to know exactly what model and operating system you have, but the answer is probably no.