Why is the Apple TV not pairing up with my new 2017 MacBook Air?

Which of the following are you trying to use this Apple TV with your MacBook Air for:

1. Streaming a video?
2. Mirroring the MBA's desktop?

Are both the MBA and the Apple TV connected to the same network (wired, wireless, or both)?

Unlike an iOS device, Bluetooth cannot be used to discover an Apple TV from a Mac. You would need a Wi-Fi connection to stream from your notebook to the Apple TV.

Ref:

• How to AirPlay video and mirror your device's screen - Apple Support
• How to Use AirPlay Mirroring - Lifewire
• If you can't use AirPlay or mirror your device's screen - Apple Support