MacBook Air 2015 to Thunderbolt cinema dispaly

The 2015 MacBook Air has a Thunderbolt 2 port. The Apple Thunderbolt display also uses Thunderbolt 2, so it plugs in directly with no adapter needed. The Thunderbolt port on the 2015 MacBook Air (but not the Thunderbolt port on the back of the Thunderbolt display) can also be used for Mini DisplayPort.

The TB2 to TB3 adapter is needed when using the Thunderbolt display with newer Macs that have Thunderbolt 3 or 4, which uses USB-C.

The 2015 MacBook Air has a Thunderbolt port (Lightning bolt icon) so can use a Thunderbolt display with no need for any adapter.

Would this adapter work?

https://www.amazon.com/dp/B01N4FQNYW?ots=1&slotNum=1&imprToken=7ec3a8f8-a267-469b-d37&tag=macworld05-20&linkCode=ogi&th=1&asc_refurl=https%3A%2F%2Fwww.macworld.com%2Farticle%2F229510%2Fconnecting-an-apple-led-cinema-display-to-a-usb-c-macbook-or-macbook-pro-here-are-the-adapters-you.html

Do you have a TB monitor or Cinema monitor? They are different animals.

OK then then will need is a TB2 to TB3 adapter to use the older TB display. That is what I have.

Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple

You are correct. Missed the year of his Mac.