It is up to Texas Gov. Abbott. 

Via Guns.com:

Supporters of permitless handgun carry in the Lone Star State have a glimmer of hope with a new bill introduced this week — if the state’s avowedly pro-gun governor plays ball.

Republican state Rep. Jonathan Stickland proposed HB 296 on Monday to allow adults otherwise lawfully able to possess a firearm under federal and Texas laws to carry a handgun concealed or openly without a permit.

Stickland backed a permitless carry measure during the regular session, but it and a similar bill failed to make it to the floor before Texas House Speaker Joe Straus gaveled the chamber to a close. Now, with Gov. Greg Abbott calling lawmakers back to work for a special session, advocates are hopeful the governor will add the gun expansion to his list of items to focus on during the legislative overtime.

Read more here.