File > Library > Import Playlist will do it, assuming the tracks that the playlist references are all in their correct locations, though it may still depend on what created the playlist. iTunes generates fully qualified paths to each track of a playlist while other software may use relative links that iTunes can't interpret.
Every significant update to iTunes results in the database being updated with the old one archived in the Previous iTunes Libraries folder. Perhaps you would be better off attempting to roll back to your pre-upgrade library to force the upgrade to be reevaluated. See Empty/corrupt library after upgrade/crash.
See also make a split library portable and this backup tip. Ideally you would have your entire library organized on the external drive, backed up to another for security.
tt2