A family of Microsoft word processing software products for creating web, email, and print documents.
As far as I know, Word Online does not fully support true templates, *.dotx files.
However, you can modify an online document (*.docx) with the settings you prefer and use it as a "template" in Word Online. Apply the style you want to start with and modify its settings. You will have to save the document under a new name each time you want to start a new document, of course.
In most cases, it is safer to use the full, locally installed version of Word for Windows (or Mac OS) to edit documents, especially longer documents.