Slice away the bottom of the orange so it sits steady on the cutting board. Working from top to bottom, slice off the peel, leaving behind most of the white pith. Finely dice half of the peel strips; discard the rest or save for another use. In a small saucepan over high heat, combine the diced peel and the water. When the water comes to a boil, lower the heat and simmer for 10 minutes. Meanwhile, squeeze all the juice from the orange and set aside.Strain and set aside the blanched orange peel.
In a medium saucepan, add diced apple, cranberries, orange juice, blanched orange peel, sugar, cinnamon, and cloves. Bring to a boil over high heat; then reduce the heat to low and partially cover the pan. Simmer gently, stirring occasionally, until the sauce thickens, the apple is tender, and the cranberries have burst, 10–15 minutes.
Transfer the cranberry sauce to a heatproof bowl and let cool for 1 hour before serving.
This cranberry sauce can be made up to two days in advance. If making ahead of time, cool, cover, and refrigerate until ready to serve.