If you are adding it to a server where you can login with a username/password, use ssh-copy-id
:
ssh-copy-id -i ~/.ssh/my-key.pub [email protected]
But if you only login with an existing SSH key, you’ll need to do it manually:
cat ~/.ssh/my-new-key.pub | ssh -i ~/.ssh/my-old-key [email protected] 'cat >> .ssh/authorized_keys'