That depends. Do you have them assigned to an actual tag field, or set as "save to MusicBee database only"?
If the latter, I suggest using a second custom tag to copy them into the files (just to be sure there's no data lost in the process).
You can check what's actually stored in the files using the Tag Inspector.
Thanks for reply. So a "save to MusicBee database only" tag works only for the current library? I checked using "Tag Inspector" and I did not find the custom tags I made nor their values.
The custom tags values are still in the previous library, but not the new one.