It has been announced some time ago already, but now the integration is finally here. You can now enable the LinkedIn integration with your Office 365 (Azure AD) tenant.
NOTE the integration is turned off by default.
Then go to your Azure AD configuration blade
Access the User settings configuration blade
And finally turn on the LinkedIn account connections option – you can choose either No (default, to keep it disabled), All (to enable it for all users) or Selected (to choose for which users you want to get it enabled)
Once enabled, wait some time (as usual I’m going to say about 24 hours), then your users should be able to get the integration as shown below
When clicking on a contact name on OWA (works with incoming emails too)
On Outlook client you may have to get the Enable LinkedIn option enabled; keep in mind this option is just for the LinkedIn Resume option, not for the contact details.
At this stage it seems, the contact details as shown above are not available in Outlook client.