To request an extension for the 2024 tax return you will need to wait until the IRS has the 2024 Form 4868 finalized which is usually in either January or February. You would need to complete, download, print and mail the Form 4868. Access the form in 2025 from this IRS website - https://www.irs.gov/forms-pubs/about-form-4868
TurboTax will normally have the Form 4868 available to be e-filed in mid-March so if you are still traveling you would be able to e-file the extension request from the TurboTax Easy Extension website.
Note - The extension request gives you an additional 6 months to file the federal tax return not an extension to pay taxes owed. If you have taxes owed on the 2024 return those taxes have to be paid on or before April 15, 2025 to avoid a failure to pay penalty.
If you will be out of the country, you get an automatic 2 month extension to June 15, but to obtain this extension without having first applied for the standard extension, you must file by mail and attach a written explanation.
The best thing to do, even if you will be out of the country, will be to either e-file the extension using Turbotax online (free, usually available in March, access from any computer with a web browser or a phone app, does not lock you into filing with Turbotax); or find someplace to download, print and mail the paper form in January. Just put a reminder in your calendar.
Note that if you need to file a form 1065 for a partnership or multi-member LLC, the deadline is March 15 and you will need to apply for a separate extension from your personal return.