A sprig is generally defined as a 2- to 4-inch piece of the herb plant. You can substitute about 1/2 teaspoon of dried herb for a sprig; however, be sure to read the recipe before you decide to substitute.
Usually a sprig is suggested, rather than the dried herb, when the recipe requires that it be removed from the dish at some point.
The dried herb can’t be removed, of course, so leaving it in the dish will give the final dish a stronger flavor. If that’s all right with you, then by all means use the dried herb if you don’t have the fresh sprigs on hand.