Yes, there’s a database and people who audit access, ensure that permissions are periodically reviewed (i.e. just because you needed access 5 years ago doesn’t mean your current duties still require the same access), and other events can trigger reviews (e.g. a large amount of personal debt could make someone a greater risk).

Which department/agency maintains the database of who-has-which-clearance?

The Office of Personnel Management runs a lot of the standardized stuff, including the system which people use to submit the standard forms, but agencies have their own offices and variations:

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