Create a filter. You can do all sorts of clever things with them, including forwarding e-mail following certain rules.

From: Automatically forward emails to another account - Gmail Help

Forward all new emails

1. Open the Gmail account that you want to forward from.

2. Click the gear in the top right.

3. Select Settings.

4. Select the Forwarding and POP/IMAP tab. (Forwarding, POP & IMAP tab) (insert image here)

5. Click Add a forwarding address in the “Forwarding” section.

6. Enter the email address you want to forward to.

7. For your security, we'll send a verification email to that address. Open your other email account and find the confirmation message from the Gmail team. If you’re having trouble finding it, check your Spam folder.

8. Click the verification link in that email.

9. Back in your Gmail account, reload the page in your web browser - look for the reload icon Reload.

10. On the same Forwarding and POP/IMAP page in Settings, check that Forward a copy of incoming mail is selected and your email address is in the drop-down menu.

11. In the second drop-down menu, choose what you want Gmail to do with your messages after they’re forwarded, such as keep Gmail’s copy in the Inbox (recommended) or archive Gmail’s copy.

12. Click Save Changes at the bottom of the page.