Start by deleting your old email account by going to Settings > scroll down and tap Accounts & Passwords > Select the OLD account. At the bottom select Delete Account and then tap Delete from my iPhone
Here is a YouTube Video showing this process.
Now to add in your new Office 365 email account.
Go to your iPhone or iPad's Settings > scroll down and tap Accounts & Passwords > Add Account.
Note: If you're on iOS 10, go to Mail > Accounts >Add Account.
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Enter your Office 365 email address and a description of your account (This is how the email will show up in the Mail app. You can set this to whatever you want. Examples are: Company Email, Work Email. Tap Next. Tap Sign In
If prompted to choose an account by Office 365, select Work or School Account.
Enter the password associated with your email account. All passwords must now be 8 characters in length. If your password was only 6 characters before, you must add a 00 (zero zero) to the front of you password. Tap Sign in or Next.
The Mail app may request certain permissions. Tap Accept.
Choose the services you want to sync with your iOS device and tap Save. You're done!
Here is a video showing you these steps in case you find that helpful.