When the Non Immigrant B visa is stamped in your passport you also get 90 days to stay inside Thailand. After 60 days you return to the Immigration Office with document of your employer and apply for the 1 year Extension of Stay based on Employment.
And 30 days before that years ends you visit Immigration again with documents and apply for a new 1 year Extension of Stay and keep on doing this as long as you work for this school.
If you need to travel, you apply for or a Single or a Multiple Re-Entry Permit.
You can do this directly after the Immigration Officer stamped the 1 year Extension of Stay inside the passport.
If you leave Thailand and come back into Thailand just before the Enter before/Valid until date of the visa you get a new 1 year of stay OR until the validity date of your health insurance.
You can not change into another Non Immigrant visa inside Thailand.
You may apply for a 1 year Extension of Stay if you can meet the requirements at your local Immigration Office.
a New Non Immigrant O-A visa can only be obtained in the US as you have residency there.
There are NO new requirements to apply for a Non Immigrant B visa and even in Covid times there was never a rule that re-entry permits are no longer needed or even issued.
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Thanks for letting us know you got a 30 day Extension of Stay based on being unable to travel. What kind of permit to stay you had to be inside Thailand and how many times did you already applied for Extensions of Stay?