In Texas licenses are issued by the state Department of Public Safety, not the county sheriff. There is an online application at the above link. You have to take an initial course in Texas, plus a simple shooting test, taught by a DPS approved instructor. There are plenty of instructors on this forum, and plenty more as well. I believe the DPS site lists them some place, and you can ask around where ever it is you are going to live.
You can carry on another states carry permit as long as Texas recognizes it even if you are a Texas resident, but I don't know how NC treats your license if you change from resident (of NC) to non-resident. Can you just file a change of address, do you have to pay some fee for a new license with a new address?
Texas CHLs also have your Driver's License number or State ID number on them, which is why I posted the links to the DL pages. You can drive on your NC DL for up to 90 days after taking residence here. You might find the paperwork process and fees simpler if you just get your TX DL soon, and then your Texas CHL sometime afterward.
http://www.dps.texas.gov/DriverLicense/ ... otexas.htm" onclick="window.open(this.href);return false;
http://www.dps.texas.gov/DriverLicense/" onclick="window.open(this.href);return false;
Texas has concealed carry only for the moment. It is a crime in the Penal Code if:
It is not a crime if your coat blows open and someone sees the gun, but you need to make a reasonable effort to conceal it.PC 46.035 (a) A license holder commits an offense if the license holder carries a handgun
on or about the license holder’s person under the authority of Subchapter H,
Chapter 411, Government Code [Concealed Handgun law], and intentionally displays the handgun in plain
view of another person in a public place.
There are open carry bills being considered in the Texas Legislature right now, but even if passed they will not likely become effective before 1/1/16.
Welcome to Texas!