It won’t. Texas already has both open and concealed carry laws in place. These laws will not be affected as they were voted on and passed by the Texas State Legislature. An individual may currently carry openly (or concealed) if they first acquire a ‘License to Carry’ or LTC. There are restrictions on the kinds of guns an individual may carry on them in public, such as shotguns and rifles, however after the independence act is passed, it is possible that these could be modified without federal government gun laws influencing Texas State laws. However, any modification would require passing a bill by a majority of the collective Texas State Legislature.
While laws regarding this topic within Texas are not yet in place, the law will likely match the US laws on the topic. Those being