Step 1: Please open Outlook on your mobile device: 

Step 2: Please click on your profile icon in the top left corner:

Step 3: Please press on the settings wheel/gear in the bottom left corner:

Step 4: From the settings menu, please select "Contacts":

Step 5: Please toggle the "Save Contacts" to On:

Step 6: Please choose "Save to my iPhone":

Step 7: Please press Allow when prompted:

The toggle for "Save Contacts" Should now be set to On: