If I add a new email address to a microsoft account then unlink the old address, can I use it to make another account later?

Yes. If the address being removed is from a non-Microsoft domain, such as a third-party email address, it usually becomes immediately available to be added as an alias on another Microsoft account after removal.

Key limits:

1. This applies to non-Microsoft domain addresses.
2. An email address cannot be associated with two Microsoft accounts at the same time.
3. If the address is already tied to another Microsoft account, Microsoft will show that it already exists and another email or phone number must be used.
4. This is different from Microsoft-domain aliases like @outlook.com, @hotmail.com, @live.com, or @msn.com. If one of those is removed, it is permanently deleted and cannot be associated with any Microsoft account again.

To do this safely:

1. Sign in to Manage how you sign in to your account.
2. Add the new email address first.
3. If needed, make the new one the primary alias.
4. Remove the old third-party email address.
5. After that, the removed third-party address usually becomes available to use on another Microsoft account.

References:

• Add or remove an email alias in Outlook.com
• Change the email address or phone number for your Microsoft account
• Why do I get the message "Microsoft account already exists" when signing into Microsoft services with my account for Skype?