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.
Elgato Gaming Devices Can't Use 4K Video or HDR Colors
Elgato Gaming devices cannot passthrough, capture or stream 4K or HDR video.
Thus, if you want to use the PlayStation 4 Pro with an Elgato Gaming device, you must set it to output 1080p or less, with HDR turned off.
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.