I have a Basler 24V 40VA 60Hz Class 2 HVAC transformer that is not putting out 24V. Checking 120V going in but nothing coming out. Looking to replace part but it seems to be vintage today. Can any transformer of these specs be used for replacement?

Very common transformer and is commonly available. Just be sure the VA is equal or greater than 40 VA.
Many AC's use 240 vollt primary and 24 volt secondary, NOT 120 Volt Primary.