What cable do I need to connect a new MacMini 2 with thunderbolt 4 to an iMac dated 2013 with a thunderbolt connection?

The new Mac mini does not support using the iMac as a display in Target Display Mode.

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

If you have a new M2 Mac mini, then you need to use an aftermarket display to the Mac mini.

see > Connect a display to Mac mini - Apple Support

2013 iMacs have Thunderbolt 1 ports.

You could connect the two Macs with the aid of a $50 Thunderbolt 3-to-2 adapter and a $30 Thunderbolt 1/2 cable for data transfer purposes, but not for Target Display Mode ones. So you might as well save the $80.

If you are trying to use the 2013 iMac as a monitor for the Mac mini, it's not possible.

Wadsworth2023 wrote:

Yes, was hoping I could use my iMac as a monitor.

Thanks for letting me know it’s impossible.

You're welcome.