Place a large zip-top plastic bag inside a 4-cup measure. Pour drippings from turkey roasting pan into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings to measure 2 cups, stopping before fat layer reaches opening. Reserve 2 tablespoons fat in bag; set aside.
Combine water, shallots, carrot, and turkey neck in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 30 minutes. Strain cooking liquid through a sieve over a bowl, reserving 3/4 cup cooking liquid. Discard solids, reserving turkey neck. Remove meat from neck; chop. Add meat and cooking liquid to defatted 2 cups drippings in 4-cup measure.
Heat reserved 2 tablespoons fat in a medium saucepan over medium heat. Add mushrooms; sauté 2 minutes. Add flour; cook 1 minute. Gradually add cooking liquid mixture; cook 10 minutes or until slightly thick, stirring occasionally. Remove from heat; stir in jelly and pepper.