I do not know about any shields that have been verified to work with NCS and nRF5340, but this kind of shields typically communicate over SPI. If you are willing to write a driver for the shield, most shields should work.
In Zephyr, there is support for a PHYTEC link board ETH shield, which contains an Ethernet chip (ENC424J600). This shield was designed for use with the Reel Board, which is based on nRF52840. This would be my best bet for the easiest route to get something up and running with nRF5340 as well, since it is already supported in Zephyr/NCS.
Another popular Arduino Ethernet shield contains the Wiznet W5x00 chipset, but I cannot find anything about support for this in NCS/Zephyr yet.
