How can I use T-Mobile unlocked iPhone with different service provider?
If it's unlocked, you don't need to activate it first. Simply switch out the T-Mobile SIM card and insert any SIM from a GSM carrier (basically anything but Sprint or Verizon in the US) and the device should work.

If you are curious, you can open the settings app and tap General, tap About then tap Carrier to update the carrier settings for the new carrier OTA. You can update carrier settings over USB with iTunes as well.