A couple of years ago a law was made that made it illegal to unlock cell phones, even after the 2 year activation period unless done by the proper carrier.
This is ridiculous as after the 2 year contract of owning the phone you should be able to do anything with that phone! Luckily their is some resistant and may be reversed, hopefully sooner than later!
Your Galaxy Note 3 needs to be rooted. Use these guides to root the AT&T and T-Mobile Galaxy Note 3.
Due to legal issues we cannot post a guide here, but you can follow a step by step to SIM unlock the AT&T and T-Mobile Galaxy Note 3 at the XDA forum.
This guide (link above) is very easy to follow and can be completed within minutes for free! It has been confirmed by many users and both data and voice work with the SM-N900A AT&T and SM-N900T T-Mobile when used on another carrier.
It has also been confirmed that the unlock stays after you do a factory reset, most likely making this a permanent solution and not just a software fix.
Credits - XDA
Like Our Facebook Page to Help Support Us! Thank You!