Upload the vtt file using the WordPress uploader to add it to the media library like you would with any file. Then select the video attachment you want to subtitle and click on the “Add track” button under “Subtitles & Captions”
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That will add several fields including one that allows you to select the vtt file from the media library or you can manually enter the URL.
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Set the track type and fill in the language code and label fields to customize the way the player displays the text track options. You can add several tracks if you need to.