In medium saucepan, combine giblets and enough water to cover. Add celery, onion, salt and pepper. Bring to a boil. Reduce heat to low; simmer 1 to 2 hours or until giblets are tender.
Drain giblet mixture, reserving broth. Set broth and giblets aside; discard celery and onion.
Remove turkey from roasting pan. Remove 1/2 cup drippings. Reserve remaining drippings in 2-cup measuring cup; add broth to make 2 cups. Set aside.
Place 1/2 cup drippings in large skillet or roasting pan. Stir in flour. Cook over low heat until smooth and browned, stirring constantly. Gradually stir 2 cups broth mixture into flour mixture. Cook until mixture boils and thickens, stirring constantly. If desired, chop giblets and add to gravy. Add salt and pepper to taste.