We need new handleset for front door. The old one measures 6 & 3/4 between holes and the new Schlage handlesets are much longer. What can we use to cover the hole at 6 & 3/4?

If it is a metal door you can buy a cover plate at HD or Lowe's. If it is a wood door you can cut a wooden plug with a circle cutter or hole saw and glue it in, fill with wood putty and repaint.