Mag Safe to Mag safe 3

I do not know of any adapters to go from MagSafe 1 or 2 to MagSafe 3. There are some third-party adapters that claim to go from MagSafe 1 and 2 to USB-C, but I don't know how well any of them work. Even if you found such an adapter that worked, you'd still be talking about a separate "power" cable from it to your Mac – not a single cable to carry video and power. So you might as well use your MacBook Air's power adapter and cable in preference to the display's.

If this is an 27" Apple display, please make sure to correctly identify it. There are two old 27" Apple displays that have cables with Mini DisplayPort connectors.

• The Apple Thunderbolt Display (model A1407) has a hydra cable with TWO heads: Thunderbolt and MagSafe. This is old-style Thunderbolt that uses a Mini DisplayPort connector. To connect this display, you will need an Apple Thunderbolt 3-to-2 adapter. A USB-C (male) to Mini DisplayPort (female) adapter will have the correct physical connectors but will NOT pass the correct type of signal.
• The LED Cinema Display (model A1316) has a hydra cable with THREE heads: Mini DisplayPort, MagSafe, and USB. For this display, you will need a USB-C (male) to Mini DisplayPort (female) adapter. Apple's TB3-to-TB2 adapter does NOT know how to present a plain DisplayPort signal on the TB2 side, so if you use it, you will get "No signal." You will also need to connect the USB cable to your Mac to control the brightness of the monitor.

Another way of telling these displays apart is that the Thunderbolt Display has FireWire 800 and Gigabit Ethernet hub ports; the LED Cinema Display doesn't.

If you have a Thunderbolt Display whose video cable is bad or flaky, you can try bypassing it by getting a TB 1/2 cable, and running that from the Apple TB3-to-TB2 adapter to the TB daisy-chaining port on the display.