Apple Watch 7 sim card

You'll move the service from your current watch to your new watch. You don't move a physical sim card.

See these this link:

Set up your Apple Watch - Apple Support

In the transfer process, you'll be asked if you want to keep your current cellular service since you will choose setting up your new watch from the backup of your previous watch. You'll also be asked if you want to use Quick Start which is so simple as it automatically transfers data from your previous watch to your new watch using your iPhone.

As lobsterghost1 says, there is no physical SIM, only the eSIM which is pushed from your network. Be aware that some networks have to enter the new watch EID manually to activate it, others are more automated and you can trigger the transfer yourself. If it doesn't go easily just phone your network and they should get you up and running. If you need the EID it is on the box label and they might ask you to read it over the phone for a manual setup.

Also be aware everyone is trying to activate new watches at the same time. Downloading the eSIM configuration to my new Apple Watch took about 2 hours yesterday after the network tech said she had setup her end and accepted it. Be patient!