Place cinnamon, cloves and peppercorns in a large square of cheesecloth. Gather ends and tie securely.
Combine cider, 1 cup water and sugar in a large pan. Bring to a boil over high heat, stirring to dissolve sugar. Reduce heat to medium, add spice bag and simmer without stirring until reduced to 1 cup, about 30 minutes.
Add fresh cranberries, bring back to a simmer and cook until softened, 5 to 7 minutes. Cool slightly.
Remove and discard spice bag. Transfer cranberry mixture to a food processor, add dried cranberries and zest and pulse until coarsely chopped. Chill before serving.