It could be three possible reasons.
The first reason is that the APN (Access Point Name) has not been set up. Usually for phones directly bought from a cellular provider shop, have the APN already built in and thus is not entered. Setting up an APN is usually what is done when BYOD/switching to another cellular provider. By putting a sim into another cellular device, you may need to enter in the APN.
If the APN is already setup, then it could either be the IMEI (International Mobile Equipment Identity), which is different for every phone (like how every network interface has a different MAC address). It could be that the ICCID (Integrated Circuit Card ID), which you can find printed on your SIM card, is locked by your cellular provider to the IMEI number of your phone. This is typically done by cellular providers to prevent the use of stolen SIM cards.
The last reason I can think of is that your new device is not on the list of devices that are supported by the cellular service provider. Just like how a MAC address can tell the manufacturers name of the network interface card, the IMEI number does the same if not more than just the manufacturer. The IMEI number can also tell not just the manufacturer, but the model of the device as well. If the IMEI of the device that you just put the SIM into, states a model number not on the list of supported devices, it may not let you connect completely or at all onto the cellular network. This is even if your device supports the cellular bands for that network.