Can I connect old iMac as monitor for my Mac mini M4 Pro?

No. A Mac mini would be too new to use Target Display Mode, the only real solution for using a Mac as a display for another system:

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

There are third-party solutions such as Luna Display, but they are only suited for uses where there will not be fast motion and where lag time is not an issue, such as for tool palettes for an app. I think you'd be happiest just buying a new monitor.

Regards.

Blajet011 Said:

"Can I connect old iMac as monitor for my Mac mini M4 Pro?: Hi, Apple i have an old iMac 2013 with thunderbold and i'd like to buy a new Mac mini m4 pro. My question is can i connect my old iMac as a monitor for my Mac mini m4 pro?"

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No. But, if your goal here is to use an Apple product as an external display, you can use a few particular adapters for an Apple Cinema Display: Configuring a USB-C Only Mac with a 30-Inch Apple Cinema Display - User Tip

a new monitor for the mac mini would use a fraction of the power of an imac acting as target display if it was supported so you'd save on your electric bill and save the environment by getting a new monitor and recycling the imac or passing it down to a friend and or relative.

That 27" 2013 iMac's screen has a resolution of 2560x1440 pixels.

27" 2560x1440 pixel monitors went for $1000 – $1200 when the first 27" iMac came out in Late 2009. These days, you can get 27" 3840x2160 pixel monitors with IPS panels and near-100% coverage of sRGB for as little as $300 – $350. 27" 2560x1440 pixel monitors with IPS panels and near-100% coverage of sRGB for about that, or maybe a bit less.

Take it from someone who actually owns a late 2013 27" iMac that it cannot be used as a display for any Mac manufactured from 2020 to today.

The only way to do it is to gut it and do some DIY stuff to make it a display (Google the internet for ways to do it).

No, the new Mac mini does not support using the iMac as a wired display.

If you get a new Mac mini, then you will need an external display.

see > Connect a display to Mac mini - Apple Support