Gmail lets you automatically forward incoming mail to another address. Please refer to the official URL on "How to forward mail to another account".

Note:
  1. If an invalid email address is used for email forwarding while 'Delete a Mail copy' is selected, all your emails will be lost.
  2. User should clean up the mailbox regularly, particularly when 'Keep local copy' is checked. Otherwise, you may encounter problems when email usage has exceeded the quota limit.