Constitutional carry means carrying without a permit. It is called that because the constitutional guarantees of the right to keep and bear arms are your permit.
The Republican Party of Texas made constitutional carry its top legislative priority in 2016, yet not a single state senator introduced a bill to implement it in the 2017 legislative session. And the governor refused to add it to the special session. This year, the delegates to the GOP state convention once again made it the top legislative priority.
If you want to see forward progress on this Republican platform item, you are going to have to vote for Libertarian Tom Glass.