If I broke my iPhone can use the same SIM card for my new one?

I broke my iPhone but I saved my SIM card to keep my number thinking i could just insert it into my new one that I bought on eBay unlocked but once I did it said no service. Does this mean I have to get a new SIM card?

Contact the network service provider, they will arrange for a new sim to be sent out.

It might be a security procedure to help make stealing mobile devices less attractive to thieves.

It sounds like the phone is either locked or not compatible, or needs APN settings entered. Your carrier may have information online for the APN settings. They can also tell you if the phone can work on their network.