What is the version of the Outlook client application?
1.Go to the Outlook -> File tab -> Office Account -> Under User Information, find Connected Services.
Please check whether the site which contains the contact you want to connect is listed under Connected Services. If not, please add it.
2.In the Outlook -> File tab -> Make sure in both Info and Office Account, you have logged in with the account has at least write permission for the SharePoint contact list.
3.In the Outlook contact page, click Type Exchange Password&Connect, re-enter the Microsoft account credential.
4.Account Settings -> SharePoint Lists -> Double click the contact list -> Untick "Display this list on other computers with the account" and Update Limit. And make sure has write permission.
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