iPhone and Outlook 365 contacts not syncing

Good morning all -

I have an iPhone and Outlook 365.  I use the iPhone native contacts / calendar / email apps.  I use Outlook on my laptop.  I use a live.com account for my calendar and contacts.  I do not use the Outlook app on my phone.

When I make a calendar item it immediately syncs with my phone, regardless of whether I made the appointment on the phone or on the laptop in Outlook.

HOWEVER the same is not true with Contacts. 

1. Contacts I make or edit in Outlook on my laptop sync right away in the phone.
2. Existing contacts that are edited on the phone sync right away in Outlook.
3. New contacts made in the phone do not sync.
4. If I edit the new iPhone contact it still won't sync.

What is going on and how can I fix this?  This is happening on two phones in my family.

Thanks for any help,

Chris