It's best to renew your passport before your visa run, as renewing the passport will not prevent you from using it for a visa run. You can travel with both your old and new passport with a valid visa for travel to the United States. This allows the passport renewal to be underway when you return to begin the work visa process, and your existing passport will still be valid for your visa run.

Here's a more detailed breakdown:

Renewing your passport:

You can apply to renew your passport at any time, including before it expires.

Visa run:

Renewing your passport doesn't prevent you from using your current passport for a visa run. You can use your old passport in conjunction with your new passport if your visa is still valid.

Returning for work visa:

Having your passport renewal process underway will allow you to return and start the work visa process with your new school sooner, once the new passport is issued.

Work visa:

Your new school should be able to assist you with the work visa application process. They may have specific requirements or procedures for hiring foreign teachers.

To summarize:

1. Renew your passport:

Start the passport renewal process as soon as possible to ensure it's underway before your visa run.

2. Proceed with your visa run:

Your existing passport will still be valid for your visa run, even if you have applied for renewal.

3. Begin work visa process:

Upon returning, your new school will guide you through the necessary steps for your work visa application.