In a new document, type something.
Observe the Style. I expect it is the normal style.
Use the dialog launcher in the style area to bring up the Styles Pane.
Right-click on the normal style in the list and pick modify.
Click on the Format button and pick font.
Turn off the underlining.
OK
OK, again
Click on the button to save in New documents based on this template.
OK
Then close out Word. You should get a query about saving changes to the template. You want to say yes.
Start a new document. The underlining should be gone.
If not, see
Add-Ins in Microsoft Word.