If you’re not logged in elsewhere and you’ve lost the smartphone with the authenticator, done a factory reset, or had it stolen (basically, if you no longer have access to it), or if the above method didn’t work, you won’t be able to recover the authenticator.
What you can do now is restore access to your account. If it’s an account with a major public service (e.g., Google, Facebook, Instagram) and your account is linked to your e-mail or phone number, you can easily restore access using an alternative authentication method.
To do this, start the account login process by entering your username and password, and when you need to enter a one-time code from the authenticator app, look for a “Try another way” (or similar) link.
Select the most convenient option — most services can deliver the code by text, voice call, or e-mail —and wait for it to arrive. It shouldn’t take long, and soon you’ll be able to sign in to your account.
If the loss of the authenticator blocks your account access, for example with a corporate or small public service that lacks an automatic procedure for restoring access, contact a local administrator or support service and explain what happened. You’ll most likely need to prove you are the real owner of the account.
When you are finally able to log in to your account, link the authenticator to the app on your new smartphone — and so as not to have to repeat everything the next time you lose your smartphone with authenticator app, create a backup right away.