In order to navigate to your catalog on external drive, hold down the Option/ALT key while launching Lightroom Classic.
Now you should see a screen that prompts you to select a catalog. Click on "Choose a different catalog" and navigate to your external drive.
Also, which version of Lightroom are you using and what is your computer's OS? I am assuming that you are using Lightroom Classic, please confirm so that we can move this discussion to the Lightroom Classic community.