using an older iMac as a second display for an airmac laptop
what kind of cord would I need to connect an older iMac desktop as a second display for a new airmac laptop?
If the new MacBook Air is truly new, i.e. 2020 or 2021, you can't. The following is from this Apple document: Use your iMac as a display with target display mode - Apple Support
The following older iMac models can be used as an external display when plugged into another older Mac model.
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.
