Janee, depending on the design of the quilt, I would either try to remove the old binding or, if it's in REALLY bad shape, maybe even just trim it off if it won't mess up the design of the top, and apply a new double folded binding as if it were a new quilt. If you do decide to just trim it, I would stitch a line of basting or stay-stitches around the perimeter that the new binding will cover BEFORE trimming off the old binding. I've done it both ways with success. Good luck!