Each and every person has two sets of teeth. One set is the baby teeth. They fall out at certain ages and stages in a child's life. Permanent's grow in at certain ages and stages. However, should situations arise, such as a bad permanent, a broken permanent, or a loose permanent tooth that would require a permanent to be removed, that permanent does not and can not be grown back. There are solutions such as partials and dentures that can replace the permanent, but there will always be a gap where the permanent used to be.
My husband had to have a permanent removed because it was abscessed. It never grew back. It not noticeable because it is in the lower back of his mouth.
But, like MarkDavisMD pointed out, new permanents can not ever be grown back.