I use a hot glue gun and very sparingly at that.
When working, the album cover should be placed on a hard clean surface and a book or other heavy object placed on the freshly glued seam so it sets properly.
At one time I used Elmer's white glue and it works, but if the least little bit too much is applied it squeezes out and binds the front and rear of the album and cannot be removed.
Before you use any glue, clean the area well, peeling away all the excess so the new bond is working from fresh paper.
It should go without saying, the LP is put away for this entire operation and if you wish to be extra cautious you can insert a spare dust sleeve inside the art work cover before beginning to provide one additional layer of safety.