I'm not sure that I understand your configuration.
See if this helps https://support.focusrite.com/hc/en-gb/articles/206849269-What-type-of-Thunderbolt-do-the-Clarett-Interfaces-Use-
If you have a Sam Ash or Guitar Center near you, you might want to talk to them.
My understanding was that the MacBook Air had a mini DisplayPort/Thunderbolt 2 jack built in. I didn't think that you could install extra cards in the MacBook Pro and MacBook Air. Therefore, I'm not sure what you mean by a Thunderbolt audio card on your MacBook Air.
I'm wondering if your reference to a Thunderbolt audio card is referring to an audio interface such as the FocusRite Clarett. (See article above.) I installed a FocusRite Scarlett audio interface (USB interface) to my brother-in-law's MacBook Pro. The only thing that I had to do was install the driver software from FocusRite and GarageBand recognized the box as soon as I connected the Scarlett to the MacBook Pro with a cable.
I'm wondering if you suffer from the same confusion that my brother-in-law had. He thought that loading the software would result in a user application being installed on the Mac or perhaps some extra preference panels appearing under System Preferences. There is a standard API on MacOS for handling audio devices. Installing the driver provides the MacBook with information on how to recognize when the FocusRite box is attached and the software components for connecting the box to the CoreAudio library. He was very confused. When I realized what was happening, I simply plugged in the Scarlett box and started GarageBand. When I looked for audio inputs and outputs, all the jacks on the FocusRite Scarlett appeared. I assume that the same would apply to other brands of audio interfaces.
If you don't have the driver software, don't worry. You can download it from the vendor web site. That is actually preferable since it insures that you have the latest version.
