Dropbox doesn't offer automated triggers quite like that, but Dropbox does offer an API you can use for listing, uploading, and downloading files, among other operations. You could use it to program your own custom automation. You can find everything you need to get started with the Dropbox API, including documentation, tutorials, and SDKs here:
For example, you can list files/folders, and then stay up to date with further changes, using:
You can also get notified of changes using webhooks:
And you can download files using:
By the way, those are links to the documentation for the HTTPS endpoints themselves, but we recommend using one of the official SDKs if possible:
Those have corresponding native methods for the HTTPS endpoints.