Unfortunately the note 3 has been out for nearly five years. The last major soft ware up date was lollipop (Android L) we are now just a few months from Android P. In short all software and security patch services for the note 3 have ended. Usually support is only good for two years. If you want updated software you either going to need to get a new phone or install a costume Rom.
Hi there and thanks for posting. joe1994 gave some great info already, I'd just like to add that T-Mobile isn't able to guarantee another carrier's device will get the update. Changing the software on the phone yourself is an option, but not one T-Mobile recommends. Honestly, your best bet is getting a new phone if you're looking to have the latest software.