Is it possible to get the share link for a file which has been uploaded to dropbox?

Here's a simple example that shows how to use that method:

try {
    SharedLinkMetadata sharedLinkMetadata = client.sharing().createSharedLinkWithSettings("/test.txt");
    System.out.println(sharedLinkMetadata.getUrl());
} catch (CreateSharedLinkWithSettingsErrorException ex) {
    System.out.println(ex);
} catch (DbxException ex) {
    System.out.println(ex);
}