Connect my iMac (2021) to my Macbook Air (2017) to use as a monitor?

1 Mba 2017 as an extended display

• only software workarounds available, none as a hardwired display. No classic Target Display Mode.
• Remote desktop, such as TeamViewer and Anydesk, is the easiest solution. And, to extend rather than mirror the source, you need to plug a dummy display dongle to the iMac, i.e. USB-C EDID Emulator, or one with a HDMI/DP/MDP connection and an adaptor, at a cost of $5-20 in total. This solution is good for Mba 2017 as it does not have the Retina display and the perceived resolution degradation is minimal.
• Airplay based 3rd party software. Duet Display is very good, with great documentations. AirServer works similarly as Airplay, and supports *extending* the source, yet has some limitations of not displaying certain content/formats.
• Mac OS has a native function to allow you using another Mac as an Airplay Receiver, and/or work with 2 Macs seamlessly as one integrated workspace via Universal Control. Without OS level mod, these functions requires Mba 2018 or later, even though the hardware of your Mba 2017 supports these features.

2 Linking iMac 2021 and Mba 2017 for data sharing

• Using iCloud or other cloud services, you can share and sync content from multiple devices.
• Set up File Sharing between your devices locally under the same network. No hardwire required.
• Set up Thunderbolt Bridge under Network settings to physically link 2 Macs - with good bandwidth. You need a costly Thunderbolt 2/3/4 cable and adapter for this, not a USB-C one.
• Set up a NAS or something similar (Apple Time Machine Capsule) so that you can share content there in real time.

Better to know your specific use case in terms of screen and file sharing so that I can make more relevant comments.

What format/content/workflow that you plan to share?

dearcharlie wrote:

I have a Thunderbolt 2 to USB-C lead and that doesn't seem to be able to connect them.

Are you talking about an Apple Thunderbolt 3-to-2 adapter? That might let you establish a data connection (for IP-over-Thunderbolt, or possibly for Target Disk Mode), but it wouldn't let you use the MacBook Air as a second "hardware" monitor.

Or are you talking about a USB-C to Mini DisplayPort adapter? The Thunderbolt 2 port on the 2017 MacBook Air can double as a Mini DisplayPort output, but it is not designed to accept Mini DisplayPort input.

Either way, the MacBook Air is not designed to act as a "hardware" display, so the best that you could hope for is some software solution. Given how cheap 24" 1920x1080 monitors with IPS panels and near-100% coverage of sRGB are these days, it's probably not worth spending too much on something like Duet Display or Luna Display just to reuse an old 13" 1440x900 laptop screen. (And a real monitor with multiple inputs could potentially serve as a second screen for both of your Macs on an as-needed basis.)

You can't do that with your Macs.

not using the old target display both macs are way too new for that

try reading Set up your Mac to be an AirPlay Receiver - Apple Support

or try Duet Display or Luna Display.