Hi there, you can activate a LinkedIn sharing button by dragging it to your Enabled Services area. We have a guide to adding sharing buttons here:
http://en.support.wordpress.com/sharing/
Head over to Settings > Sharing to get started, and just let me know if you need any help with it:
https://buildingcorporateculture.wordpress.com/wp-admin/options-general.php?page=sharing
Here’s a screenshot of exactly what you need to do:
https://cloudup.com/cJWxFSEBzDd
Once you’re done, click Save Changes and you should be good to go.