Verizon is a CDMA carrier, and operates on a different technology than AT&T and T-Mobile (which are GSM). However, you should still be able to use your unlocked Verizon 4G LTE device on AT&T or T-Mobile, as most handsets will be compatible with both carriers’ LTE bands.
Can you put a Verizon SIM card in an AT&T iPhone?
A Verizon SIM should not work on an AT&T iPhone 7 Plus unless it is a factory unlocked phone. Next there is carrier unlocked and that means the phone has been unlocked from the carrier and will work on one of the two types of networks. It will either work with all CDMA networks or all GSM networks but not both.