Squeeze the juice from the orange half and set the juice aside. Remove the membrane from the inside of the orange shell and discard. Cut the shell into small dice. Put into a small saucepan with the water and bring to a boli, and cook for 10 minutes. Drain and set aside.
Peel, quarter and core the apple, then chop into small pieces. Place in a saucepan. Sort the cranberries, discarding any soft ones. Add to the apples along with the reserved diced orange peel, the reserved orange juice, the sugar, cinnamon and cloves. Bring to a boil, reduce the heat to a simmer and cover partially.
Simmer gently, stirring occasionally until the sauce has thikened, the apple is tender and the cranberries have burst, 10-15 minutes. Transfer to a bowl and let cool before serving. Or cover and refrigerate; bring to room temperature before serving.