It appears that the CalDigit TS4 and CamLink 4K may cause freezing issues when connected together. To fix this, users have reported that they had to plug the CamLink 4K into a Windows computer and use Elgato’s 4K Capture Utility to change the USB Transfer Mode from Automatic to Isochronous.
Additionally, some users have reported that plugging the CamLink 4K into a Thunderbolt port on the back or one of the front USB-C ports of the TS4, in conjunction with the Isochronous fix, has helped resolve the freezing issue.
To fix this problem, I had to plug the CamLink 4K into a Windows computer and use Elgato’s 4K Capture Utility, which isn’t available for Mac, and change the USB Transfer Mode from Automatic to Isochronous, which maintains a constant rate of transmission.
CalDigit TS4 review: king of the Thunderbolt docks - The Verge
The video signal freezes or jerks and won’t start again. This happens in Zoom, Camtasia, and other apps.
Something must be happening where the TS4 is not passing the signal correctly through the TB4 cable to my MacBook Pro.
Camlink 4k HDMI not working with CalDigit TS4 : r/elgato
Support – CalDigit
If you haven't already, try plugging into a Thunderbolt port on the back or one of the front USB-C ports. Those are using higher priority controllers on the TS4. In conjunction with the Isochronous fix mentioned by OP, this has helped resolve this behavior for many TS4 users.
Camlink 4k isochronous annoying green flicker : r/elgato
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TS3 Plus | Thunderbolt 3 Dock – CalDigit