Defense & Borders
Would Texas need a navy or coast guard for the Gulf?
Texas would maintain a maritime force for its Gulf coast, and the most likely shape of it is a coast guard built for the real missions, search and rescue, law enforcement, environmental and port protection, rather than a blue-water battle fleet Texas does not need. Texas already has the seed of this capability in place.
Match the force to the actual mission
Start with what a Gulf maritime force is actually for. Texas has a long, busy, vital coastline: the Port of Houston, the largest United States port by foreign tonnage, energy infrastructure offshore, fisheries, and heavy commercial traffic. Protecting that means search and rescue, fisheries and law enforcement, environmental response, aids to navigation, and port and coastal security. Those are coast-guard missions. They are not a reason to build an aircraft-carrier navy. Right-sizing the force to Texas's genuine needs is not a limitation. It is simply how a serious country plans.
Texas already has a maritime element to build on
The Texas State Guard already includes maritime regiments, staffed in part by veterans of the United States Coast Guard, Navy, and Marines, trained for waterborne search and rescue, dive recovery, and boat operations, and they have worked alongside the United States Coast Guard and the Department of Homeland Security. That is a real, existing maritime capability under the governor's command. An independent Texas would have a foundation to grow a national coast guard from, not a blank stretch of water.
A coast guard is what the missions actually call for
Look at what a coast guard does, by its own founding charter, and the fit is obvious. The United States Coast Guard's core duties are enforcing the law on the water, maritime surveillance and interdiction, promoting safety of life and property at sea, search and rescue, and maintaining aids to navigation. Every one of those is a thing Texas's Gulf coast needs done. An independent Texas would stand up a coast guard scaled to its coastline and its commerce, focused on exactly these jobs, the way maritime nations of similar size and threat profile do.
Cooperation covers the bigger maritime picture
For the larger maritime-security questions, shared waters, trafficking interdiction, freedom of navigation in the Gulf, the answer is the same as it is everywhere in this cluster: cooperation. Neighboring maritime nations coordinate on their shared seas through agreements, and an independent Texas would do the same with the United States and Mexico, very likely as part of the broader defense relationship. Texas does not need to patrol the entire Gulf alone any more than any coastal nation does. It needs to cover its own waters well and cooperate on the rest.
A bigger maritime force is a sovereign choice for later
Whether an independent Texas ever builds beyond a coast guard toward a larger naval capability is, like every force-structure question, a decision for the future Texas government and its defense leadership, funded out of Texas's own economy as it sees fit. The honest answer today is that the everyday maritime mission, the one Texas actually has, is a coast-guard mission, and Texas is well placed to meet it. Anything beyond that is a choice, not a necessity.
The bottom line
Texas would maintain a Gulf maritime force, most sensibly a coast guard built for search and rescue, law enforcement, and port and environmental protection, growing from the maritime units the Texas State Guard already fields, and cooperating with neighbors on the wider Gulf. A larger navy is an option for a future Texas to weigh, not a requirement for security.