Nope, your new SIM card will be blank. However, if you already have an iPhone, it's not that hard to transfer contacts. You can do it a couple of ways. Assuming you don't have an iPhone, you'll need to insert the SIM into the iPhone, go to Settings > Contacts and press "import SIM contacts". Problem with that is a standard SIM won't fit into the iPhone 4S, and you'll need to cut it down / use a SIM cutter (looks like a hole puncher ... can be found on Amazon). You can take it to AT&T and they might be able to help (by flashing your contacts from your old SIM to a microSIM and importing the numbers that way).
Edit: Just saw the post above. You keep the same phone number.