Use 2017 4K Retina imac as a monitor for new Mac Book Air

Target Display Mode went away in Late 2014 when the first 27" 5K Retina iMac came out. Your 2017 iMac does not have that feature. Apple also added restrictions such that no current Macs can use any iMac as a Target Display.

See the bad news here: Use your iMac as a display with target display mode - Apple Support

Your iMac is also too old to be an AirPlay Receiver for AirPlay to Mac, a lower-quality way to use a Mac as a display.

See the bad news here: Continuity features and requirements for Apple devices - Apple Support

There are third-party workarounds, but they may involve unacceptable compromises. For instance, third-party applications to give your old iMac "AirPlay Receiver" type capability are probably based on AirPlay v1 protocol with a maximum resolution of 1920x1080 (plus the potential for lags/artifacts). Duet Display is a subscription (rental) application that would cost you $48 to $72 per year. Luna Display would likely require you to use up two ports: one for the Luna Display device (which is supposed to be connected directly to the Mac), and another for a cable between the Macs. And an article on the Luna Display site says that the product is not recommended for high motion content.

You are best off budgeting for a real display.

As for the salesperson's idea of buying a MacBook Air and returning it "within 3 weeks" if you can't use the old iMac as a display, note that the return period for computers bought directly from Apple themselves is 14 days. If you had bought a computer and then tried to return it on the 15th day, even though it was functioning perfectly, just because your old iMac isn't designed to be a monitor, the store would have been within their rights to refuse the return.

Darcy Geale wrote:

Has anyone one had a simple, tested solution where I do not have to pay an ongoing fee. EG using direct unit to unit Thunderbolt connection between two units (using USB C Thunderbolt cable iMac has two USB C slots with a lightening sign above plus an Ethernet slot). Will this work?

A Thunderbolt-to-Thunderbolt connection was part of the requirement for iMacs that

• Supported Target Display Mode, and
• Had Thunderbolt ports

but a 2017 iMac does not support Target Display Mode.

Just having a Thunderbolt connection alone wouldn't let you use the iMac as a display, especially when the iMac doesn't support Target Display Mode and the new Mac doesn't support using any iMac as a Target Display.

Sidecar lets you use a supported iPad as an extra screen for a supported Mac.

It does not let you use a Mac’s screen as an extra display for an iPad or for another Mac. That would be the AirPlay Receiver feature of AirPlay to Mac, which your 2017 iMac does not support.