To add an administrator to your LinkedIn Company Account, follow these steps
Firstly the person you want to set as an administrator needs to be connected directly with you.
Go to your LinkedIn account, then select Interests > Companies
If you already have a company established, then click on the Company name under "Manage your page".
Once on your company page, click on the "Edit" button
You will now see an area for Designated Admins.
Enter the person you wish to grant access to and select them, once complete click publish.
That's it all done.