OS X El Capitan 10.11.6 (2013-Intel) Extended Monitor

The new MacBook Pro does not support using the older 2013 iMac in Target Display Mode.

carefully read > Use your iMac as a display with target display mode - Apple Support

There are a few options like Screen Sharing, but they are not the same as using an external display with the MacBook Pro.

see > Use an external display with your MacBook Pro - Apple Support

+1 den.thed is 100% correct, your old iMac will not work as a display. Please remember that iMacs are computers, they are NOT external displays for other devices. In short, it is time to buy an external display if you want one for the new Mac. The advantages:

• No expensive cabling required!
• No software to install, de-bug, support .
• Low cost, external displays start at <$100. You can spend up to $1500 and anything in-between though. For less than $200 you can find another 27" HD display that would work perfectly well for many years.
• Simple setup.
• No maintenance and dead reliable.

Carlomtl wrote:

Hi,

We have the old iMac with OS X El Capitan 10.11.6 (2013) and recently we have purchased the new MacBook Pro Sequoia 15.1 (2023-Apple M3) are they compatible to use the iMac as extended monitor from the new MacBook Pro?

No. The 2013 iMac supports Target Display Mode – using Thunderbolt input – but Apple placed restrictions on Target Display Mode. The M3 MacBook Pro is too new to use any iMac as a Target Display.

We have tested the Thunderbolt 2 to Thunderbolt 3 USB-C connected directly from iMac to MacBook Pro is does not work using the Comman+F2 shortcuts as I read from other site.

A Thunderbolt connection is necessary – but not sufficient. Whatever "other site" you read must have failed to mention the restrictions that the source of the video must be a Mac released in 2019 or earlier, running macOS Catalina or earlier. The M3 MacBook Pro is too new on both counts.

You're welcome.