You were already allowed to have a gun in your car before this bill in Texas. Generally speaking, Texas law allows people to transport a handgun in their vehicle as long as they are otherwise allowed to possess a firearm. https://faq.sll.texas.gov/questions/42809
The new law makes it perfectly clear one can have a weapon in a car without having a License to Carry (LTC). It was fuzzy before this new bill.
You posted only the first paragraph of the old law, here is the rest of the old law dealing with License to Carry (LTC): (consider the rest in "quotes")
Generally speaking, Texas law allows people to transport a handgun in their vehicle as long as they are otherwise allowed to possess a firearm. Texas Penal Code Section 46.02 creates an offense for the unlawful carrying of handguns and in subsection (a)(2)(b), makes an exception to unlawful carry for those who are:
(B) inside of or directly en route to a motor vehicle or watercraft that is owned by the person or under the person's control.
Additionally, section (a-1) states that
only those with a Texas License to Carry (LTC) are permitted to keep a handgun in “plain view” within the vehicle. Those with an LTC must keep their handgun in a shoulder or belt holster if their handgun is in plain view.
