We have a FileMaker Server Advanced that hosts just under tables. Within those tables, there are hundreds (if not thousands) of database relationships. We just recently moved to a new location. Part of that move was implementing a new network schema and active directory. Is there a way to perform a batch update of all database relationships?

There should be no need to update anything.

Unless you are asking whether the active directory can be used to manage database access? In which case you need to look into External Authentication.