How to restrict Mail to contacts on iPhone

If you mean receive email only from people in Contacts, Apple Mail doesn’t have a “Contacts only” setting.

You can block individual senders, but for a true whitelist you’d need to set up filtering rules with your email provider.

If your main goal is just to avoid notifications from everyone else, another option is to add important contacts as VIPs and enable Mail alerts only for VIPs. Apple explains that here: Use mailboxes to organize email messages on your iPhone or iPad - Apple Support