Connectivity question re. new IMAC

A display connected to a 10 year old iMac was probably using Mini DisplayPort, not Thunderbolt. The plugs are compatible but the iMac didn't get Thunderbolt until 2011. If it is a 2011 or later iMac it will have Thunderbolt (Lightning bolt icon next to the port). If the display is Thunderbolt there will be a Lightning Bolt icon on its plug.

The Apple Thunderbolt 3 to Thunderbolt adapter will work with a Thunderbolt display but not with Mini DisplayPort, even though the plugs will fit.

For Mini DisplayPort, you need a USB-C to Mini DisplayPort adapter, such as:

https://www.uptab.com/usb-c-to-mini-displayport-adapter-4k-60hz-silver/

Likely yes but without knowing the connections the external display has we can’t tell you they would be.

New iMac use Thunderbolt 3 which is also the same as USB C. Please advise exactly what a "adapted from multi-pin" connection is, does this mean, HDMI, VGA, DVI etc???? When asking a question and requesting assistance we need specifics, please remember we cannot look over your shoulder and and we are not clairvoyant so we rely on you to write effective questions so you can get effective answers. Perhaps reviewing Writing an effective Apple Support Communities Question will provide you an idea of what we are looking for.

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Sounds like you need this adapter...

https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter