Mac Mini compatibility

If you are asking "can I use my 2013 iMac as a display for a new Mac mini" the answer is no.

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

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.

The 2013 iMac does support Target Display Mode, but must be running High Sierra or earlier.

The new Mac mini does not support Target Display Mode, because it is newer and can only run Monterey or later.

Guy Pritchard Said:

"Mac Mini compatibility: Can I use a Mac mini with my iMac : iMac (21.5-inch, Late 2013), 1 GHz Quad-Core Intel Core i7, 16 GB 1600 MHz DDR3"

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Please clarify your post:

Just how are you looking to use this with the other Mac? What issues are you having? How have you troubleshot it thus far?

Unlikely.

iMac? Too new.

Mac mini? Maybe too.

..Those abilities were in older previous models..

(But I may be mistaken. Just because mine don't.)