Would like to change where the repository database is located from local to a server copy.
Backup the database in SQL Server and SQL Restore it to the new server. Then change the Link Tracking connection information to point to the new server/credentials.
If using the Link Tracking Redirector, then the "Link Tracking/Import Services" installed on SharePoint. You will need to use Central Admin to update the connection information there. If you are doing Client side Link tracking, then you also have to change the connection information in the client.
Pay particular attention to the Permissions being applied to the database on the new server. It needs to be accessable by the Redirector if using the Link Tracking redirection, and also visible and read/writeable by the client (if using client side link tracking).