Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter adaptor
Can I use Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter adaptor to connect my Mac Pro 2013 (Late) to the LG 4k display sold by apple?
Mac Pro, macOS 11.5
ONLY if that is a geniuine ThunderBolt display.
This adapter is not compatible with displays that use DisplayPort or Mini DisplayPort, such as the Apple LED Cinema Display. Thunderbolt and Thunderbolt 2 are not the same as Mini DisplayPort 
though the ports have the same shape.
Use the Thunderbolt port of this adapter to connect your Mac to a display that uses a Thunderbolt or Thunderbolt 2 cable. For example, you can use this adapter to connect your Mac to an Apple Thunderbolt Display or LG Thunderbolt 2 display.
from:
About the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple Support
executive summary: this adapter supports ONLY genuine Thunderbolt displays, and no other display protocols whatsoever. NO DisplayPort, NO HDMI, NO Mini DisplayPort, NO USB-C, NO DVI, NO VGA.