Can I use my old SIM card in my new UNLOCKED phone?

Can I use my old SIM card in my new UNLOCKED phone?
Added (1). I bought an unlocked Galaxy S6. I am ALREADY on a plan with T-Mobile. The reason I didn't go through them for the phone is because my aunt is the account holder and doesn't believe in upgrading your phone unless absolutely necessary. Anyway. If I put my old SIM card in the unlocked Galaxy S6, would it work/keep me on my plan? If I bought a NEW SIM to use. Would I need my aunts SS or account holder ID number to call T-Mobile and get it to work? My aunt won't be too helpful which is my concern.
Added (2). And yes, the unlocked phone is for GSM bands, HSDPA bands and LTE bands.

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