I had the same question. Clarity told me it was a bug in their system right now and it will be fixed soon. That was a month ago.

There was a bug. I guess probably it is solved. Now you can connect your LinkedIn profile with your clarity account.

August 27 2019: I reached out to the Clarity Support Team because this impacts all Clarity Experts.

Here is their response:

"Apologies for the trouble on this one. Unfortunately due to a recent change in LinkedIn's policies, we won't be able to connect LinkedIn accounts for them as of now. We will notify in the near future for possible changes on this status but for now we do thank you for your patience on the matter. For now, one workaround would be to add a link of your LinkedIn account to your profile."