Before you begin: To connect a LinkedIn social account to Analytics, you need to have the role of SUPER ADMINISTRATOR of the Page.
On the BRANDS page, click on the ADD A NEW ACCOUNT:
On the next screen, you choose the social network you want to connect to the brand. In this case, it's LinkedIn Pages. Click on the "Connect" button to the right of this network.
You will be directed to LinkedIn. Enter the credentials of the LinkedIn Page Super Administrator account you want to link to Analytics and click "Sign In".
Grant the permissions requested by LinkedIn by clicking "Allow".
Then the screen will be redirected back to Analytics, simply select the desired page and click "Connect".