Using Outlook for Android in business environments for email and scheduling
This worked for me on my Samsung Galaxy S8.
Installed the recently updated Outlook app and added my Outlook.com account. (Note: I have a custom domain hosted on Outlook.com. Pretty sure you can't do that anymore, but if you are one of the legacy users like me, this will work.)
After I added my account, I went into the Outlook app and under settings, and tapped the account (named for my email address) in the Accounts section. There I enabled "Sync Contacts". Microsoft was thoughtful enough to display a note saying the sync may take up to an hour to complete but mine synced immediately.
From there, I went to the native Android contacts app to confirm that the Outlook account was now listed for sync. Tap Settings and then Contacts to Display. You should see the Outlook account listed there.
Guidance is here for both Android and iOS...