From this April, DisplayLink adapter does not work with macOS 10.13.4. When I checked displaylink.com, I've found that they released new driver, and this driver supports extended display as following:
How to enable an extended DisplayLink display on macOS 10.13.4 with 4.3 beta 3
https://support.displaylink.com/knowledgebase/articles/1854724
This version has some limitations as following:
AirPlay does not support rotation. It will not be possible to rotate a display with this solution.
The display resolutions available through AirPlay by default are 720p (1280x720) and 1080p (1920x1080). More resolutions are available if you click on "Scaled" while holding down the option key:
If you have multiple DisplayLink displays connected, there is no interface to choose which display becomes your Airplay display. If the wrong display is selected, then disconnect this display to prevent it being the AirPlay display.
Currently, after logging in, it will be necessary to unplug and replug the DisplayLink device for AirPlay to work again.