If you are adding the withdrawal address from a trusted device, your new address will be approved automatically. Otherwise, you will need to verify it via a link sent to your registered email address. After clicking on the verification link, you will then be able to use this address to make withdrawals from your Kraken account.
There is also a link in this email to lock your Kraken account, in case an attacker has compromised your Kraken account and is trying to add their own withdrawal address to steal your funds. Only click this Lock Account link if you did not authorize the addition of this withdrawal address.
The withdrawal approval link that is sent to your email will be valid for one hour, if you do not confirm your withdrawal address within that time the link will expire.