Cut each peach half into 4 slices and place in a bowl.
Combine the peach syrup, sugar, vinegar, cinnamon sticks and cloves in a saucepan over medium-high heat; bring to a boil.
Reduce heat and simmer for 10 minutes.
Pour the hot syrup mixture over the peaches.
Chill, covered, for a day or two in the refrigerator before serving.