ARD troubles targeting Ventura

Did you get the most recent version of ARD from the App Store which appears to be v.3.9.6 which says is compatible with Ventura?

Also, what isn't working? Is ARD not launching, or you cannot navigate the app, or you cannot connect to some remote Macs? If the latter, what versions of macOS are those remote Macs using? I see in the feedback comments for ARD in the App Store that to connect to older Macs you may need to click "Allow communication with older clients" in the ARD preferences/settings (less secure).

I haven't used ARD in many years, so I'm not sure how any of the new macOS security settings may affect connecting to remove Macs.

You may have already seen this but in case you hadn't:

Apple Remote Desktop User Guide for Mac - Apple Support