how use my my iMac 2013 as a second display with my MacBook Air 2021?

Cannot be done. No Mac that has been introduced since 2020 can connect to any iMac via Target Display Mode.

I can verify this as I have a late 2013 27" iMac and an M1 2020 MacBook Air and it does not work. There are no hacks, workarounds or magic wands that will make it work.

Is not possible. See:

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