Can I share Ethernet internet connection through Thunderbolt cable? I do not want to use WiFi but need to share my iMac's Internet connection (with incoming Ethernet) to my MacBook Pro, using a Thunderbolt cable.

I've connected the two in Network/sharing settings, can share files/screens etc, but the MacBook Pro does not pick up any Internet connection.

I switched on Internet sharing on the iMac, Ethernet &rarr; Thunderbolt, but no joy - any ideas?
You need to enable the DHCP server service included in macOS. Do this on the side that acts like a router (sharing side).

DHCP is what gives an IP address, DNS servers to user etc. to connected devices.