And that's all you need to do to sync your new audio to your old video! Yes, if you're new to Premiere Pro, it may still seem to be a lot of steps. but once you do this a few times, it runs rather smoothly.
And if you like the result, be sure to take the time to learn more about all the cool things you can do in Premiere Pro. Everything from home movies to major motion pictures are edited using this application.
If Premiere Pro is just too overwhelming, you can try using Premiere Rush instead as your video editing tool. However, Rush does not offer a way to accurately sync audio to other footage, so be prepared to do some manual tweaking.