If you set up your email as an IMAP or POP account, your calendars and contacts won’t sync. You’ll have to add them as an Exchange ActiveSync account. Also make sure that your email app has the correct permissions to access your calendar and contacts.
See Sync calendar with my phone or tablet if you are having sync issues when setting up your email account for the first time
If your email account is working fine on a computer, the issue may be with your email app and you’ll have to contact their support. For example, if you’re having trouble adding an Outlook.com email account to the iOS Mail app, contact Apple Support. We recommend downloading and installing the Outlook mobile app for easy calendar and email management.