If I get a new T-Moble SIM and activate it on my Google Nexus 4, then put the old one back in, will the old one still work?
This is not an Android question, but more like a generic mobile question.
But to answer your question: YES, the old one will still work. SIM cards are not tied to cellphones. So, you can always transfer SIM cards to other phones that have SIM card slots, assuming that the phone allows the network your SIM card is for. i.e. If the phone is locked to a specific network, then only SIM cards for that network is allowed. Of course, you can remove this limitation by unlocking the phone.