If you recently switched to Google email, you can transfer your old mails from your other email account.
Sign in Gmail.
In the top right corner of the page, click Settings (gear icon)>Settings.
Click the email Accounts and Import or email Accounts tab.
In the second section, click Import email and contacts tab.
Follow the given steps on the screen.
Click at Start import button.
To give you time to tell your friends or family members about your new Google email address, we’ll forward email sent to your other email account for 30 days.
Stop importing emails
Sign in Gmail account you’ve been importing to.
In the top right corner of the email page, click Settings (gear)>Settings.
Click the Accounts and Import button.
In the “Check email from other email accounts” section, click delete next to the email account you want to stop getting emails from the account.
Note: If you’re still receiving emails, check if automatic email forwarding is set up in your other email account, then do a search on how to turn it off in your other email account. If you want to delete emails that were already imported