If you are a resident of New York and only visiting Texas then to the best of our knowledge you would not be able to apply for a learner's permit to drive in TX. You would need to be a resident to obtain a permit and start the graduated licensing process in Texas.
The Texas Department of Public Safety states that a person under age 18 must show proof of driver education, verification of current enrollment and attendance in school (or high school graduation or GED), proof of social security number, as well as proof of identification to apply for an instruction permit, which is phase one of the TX licensing process. If you are a resident of New York and not Texas then the DPS would not issue you a permit.
In Texas a teen can enroll in a driver education class at age fourteen (14). At 14 years of age one can enter the classroom phase of driver education, and then the teen must be at least 15 years to enter the in-car phase. Those are the minimum ages and some schools require students to be older.
A student is not permitted to apply for an instruction permit until he or she is at least 15 years of age and has completed at least Module One (minimum of six instructional hours) of a driver education classroom program. Application for an instruction permit license requires the student to pass a Department of Public Safety (DPS) written examination and to meet all other DPS licensing requirements.
The DPS states that the legal driving age in Texas is 15 years of age, no exceptions. A TX instruction permit allows a beginning driver to operate a vehicle with someone in the front seat that is 21 years of age or older and holds a valid license. As we mentioned earlier, as an out of state teen you could not normally obtain the instruction permit since you are not a resident of TX and also you have not completed the driver education classes that Texas requires of learner permit applicants.
Even if you were somehow able to get a permit in Texas as an out of state resident you still could not use this permit to drive in your home state of New York since you are under 16.
According to the New York State Department of Motor Vehicles, the minimum driving age in New York State is 16. You cannot drive in NYS if you are under the age of 16. If you have a learner's permit or driver's license from another state, you are not exempt from this NY rule.
You must be 16 years of age or older to apply for a learner's permit in NYS. If you are under the age of 18, your parent or legal guardian must sign the consent section of your driver license application. A junior license is issued to drivers under the age of 18 and has restrictions.