When you say "database", do you mean "catalogue"? On that assumption....
In the "old" catalogue, select images you've edited and do Ctrl S (Cmd S if on Mac). In the new catalogue, select them and do Metadata > Read Metadata from File. That's it. Note that "old" adjustments and metadata will overwrite those in the new catalogue.
Alternatively, select them and File > Export to Catalog and create a small temporary catalogue on your desktop. Leave all options unchecked. Then in the new catalogue, use File > import from Another Catalogue. This will pick up more work - eg flags, history steps - than the other method.