Using your back up code/ Recovery key
Get your back-up code that you saved at the time of setting up 2FA with your older phone. This document has the recovery key that you can now use to restore Poloniex account on your Authenticator app. To know more about back up code/ recovery key, please refer to 'Step 4' of the article 'How do I set up 2FA'
You’ll need to again add a Poloniex account in your authenticator app and either manually enter the 16-digit recovery key or scan the barcode using the app.
You may now continue using your Authenticator for logging into Poloniex.