From Gmail help:
Automatically forward Gmail messages to another account
You can choose to forward all of your new messages to another email address, or only forward certain types of messages.
Set up automatic forwarding
You can automatically forward your messages to another address. You can choose to forward all new messages, or just certain ones.
Note: You can only set up forwarding on your computer, and not on the Gmail app.
The following are the few first steps, further explained at Gmail help:
- On your computer, open Gmail using the account you want to forward messages from. You can only forward messages for a single Gmail address, and not an email group or alias.
- In the top right, click Settings (cog).
- Click Settings.
- Click the Forwarding and POP/IMAP tab.
- Set a repective Filter as needed to limit the scope of forwards.
- In the "Forwarding" section, click Add a forwarding address.
- Enter the email address you want to forward messages to.
- Click Next and then Proceed and then OK.