No, you don't need to "Publish" it.
But you do need to find an old book on Lotus Notes development and read about templates. Since you state that you are new to Lotus Notes, you should not be attempting anything without having at least read one book to learn the basics about something that has been around for more than 25 years. (And not just about templates!)
If you have a separate test environment, then it's pretty certain that the organization that you are working for has been using templates as part of their process for deploying applications. You should be making a local copy of the template, backing up the template, modifying the form in the local template, then using the replace design or refresh design feature to update the database in the test environment, and then you should figure out how your organization has been managing production templates and deploying the changes to production apps, and you should follow that process.
I'm being a bit vague here on purpose. I've given you the key words, but there are many ways your organization might have been managing this You need to learn the basics first, and then use what you have learned to conform to your organization's preferred practices.
