I assume you are referring to changing the WordPress admin email address. You can change this under Settings, but you will need to receive a confirmation email with a link that you must click on to confirm the change. I assume you are referring to this email, that it did not arrive?
It should normally arrive immediately. If not, you either mistyped the email address or it was recognized as spam by your email service provider and filtered out.
Even if you find it in your spam folder, the link will no longer be valid. Instead, I would recommend changing the admin email without this email. You can do this as described here, for example: https://www.wpbeginner.com/beginners-guide/how-to-change-the-wordpress-admin-email/
This plugin may also be helpful: https://wordpress.org/plugins/admin-email-address-changer/
Once you have changed this, you should make sure that you are receiving emails from your WordPress. An SMTP plugin may help here. You can find a selection of these here: https://wordpress.org/plugins/tags/smtp/
Yeah, that’s sort of flaky. Here’s another way. In wp-admin, delete/cancel the pending change. Then, at https://yoursite/wp-admin/options.php, scroll down to “admin_email” and update the email address there. It’s immediate and no verification is required.
