can I use a 2013 late model IMac as my external display for a new MacBook Air

Hello!

Unfortunately, no.

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

iMac models introduced in 2011, 2012, 2013, and mid 2014

To use any of these iMac models as an external display:

The iMac used as a display must have macOS High Sierra or earlier installed.

The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.

The cable connecting the two Mac computers must be a Thunderbolt  or Thunderbolt 2  cable.

Jack

No. There are no workarounds, tweaks, has, or magic powders that will make it work as a display with the new MacBook Air. I know this for a fact as I own both.