Mirroring from macbook pro 2018 to iMac 2013

Follow the steps in the support document linked below to activate Target Display mode on the iMac first then connect it to the MacBook Pro.

click here ➜ Use your iMac as a display with target display mode - Apple Support

Do note, the iMac needs to be running High Sierra or earlier, and the MacBook Pro will need to be running Catalina or earlier, otherwise it will not work.

If you are trying to use the 2013 iMac as a Target Display Mode screen, there are several things wrong with your setup:

• You need a Thunderbolt-to-Thunderbolt connection, not a "Thunderbolt-to-HDMI" one (whatever you mean). That would involve a TB3-to-2 adapter and a TB1/2 cable.
• Your iMac is running something later than High Sierra.
• Your MBP is running something later than Catalina.

If any of these things are off, you won't be able to use the 2013 iMac as a TDM display. (The restrictions on the operating systems may be new, and unwelcome, but that and $3.00 will buy you a cup of coffee …)

DondiGBD wrote:

Hi and thanks for some direction however this process does not work based on the parameters of my computers - my iMac is running Catalina (post High Sierra) and my MacBook pro is running Ventura (post Catalina). Any other suggestions?

Again,

1. The iMac must be running High Sierra (or earlier) macOS versions past High Sierra will not allow the connection.
2. The MacBook Pro must be running Catalina or earlier. Ventura does not support Target Display Mode.

It will not work otherwise.

I have a thunderbolt cable to HDMI cable connected between the two but neither display is recognizing the other.

How does HDMI come into this?

From what I can see, the 2013 iMacs have Thunderbolt 1 poirts, which can double as Mini DisplayPorts. The 2018 MacBook Pros have USB-C ports with DisplayPort and Thunderbolt ALT modes.

Neither have HDMI ports, although there were HDMI ports on Retina MacBook ports from a few years earlier. The HDMI ports were strictly for video output, not video input.

DondiGBD wrote:

Yes, this process does not work based on the parameters noted above. My iMac is running Catalina (post Sierra) and my MacBook pro is running Ventura (latest os). Any other suggestions?

You Apparently missed the part where the MBP must be running Catalina or earlier.

You probably won't be able to use the old Mac as an AirPlay Receiver, either. You're running Catalina (not Monterey or later), and that iMac is not on the list of models for which AirPlay to Mac "works best."

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

System requirements for Continuity on Mac, iPhone, iPad, and Apple Watch - Apple Support