Hard to comment on your issue without seeing a picture of your project timeline. Can you post a screen shot? Are you intending the newly added clip not to have background audio below it?
The first thing to do is to make a duplicate of your project and then work with the duplicate so that your original work is preserved. Saves a lot of headache.
Depending on how complicated the audio/syncing is, one can usually add a clip to the beginning of the project timeline and have everything following it slide down the timeline in unison. It doesn't always work that way, particularly if you have numerous bits of audio syncing with the video, or have stacked audio clips. However, as long as you are working with your duplicate project, no harm done because you still have your original with it original edits. You can make as many duplicates as you want for purposes of experimentation.
Another way to do it is to export your project to your desktop, that will merge all of the edits and the sync. Then import the exported movie as one long clip into a new project. Add your new clip to the beginning.
-- Rich