The PlayStation 4 Pro (PS4 Pro) was released on November 10, 2016.
The PS4 Pro offers output at up to 4K resolutions (3840 x 2160).
The PS4 Pro also offers HDR color output as an option.
Most Elgato Gaming Devices Can't Use 4K video
Most Elgato Gaming devices cannot passthrough, capture or stream 4K video. For those devices, you must set your PlayStation 4 Pro to 1080p output, or less.
The only device that can capture 4K video is the Elgato Game Capture 4K60 Pro.
Most Elgato Gaming Devices Can't Use HDR Colors
If you want to use the PlayStation 4 Pro with most Elgato Gaming devices, you must turn HDR off.
However, the latest version of Elgato Game Capture 4K60 Pro can passthrough HDR colors. See this article for more details:
HDR Video is Supported with New Hardware and Software
You should also turn off HDCP.
Before you set things up, make sure to connect your PlayStation 4 Pro directly to your TV set or display via HDMI, without using Elgato Gaming product.
Then, visit the Settings > System section of the PlayStation 4 Pro interface, and turn off Enable HDCP.
After that, you can use your PlayStation 4 Pro with Elgato Gaming hardware.