Rinse quince; with a sharp, heavy knife, thinly slice crosswise. Place slices in a wide-mouthed 1 1/2 quart jar, arranging more attractive slices veritcally.
Add cloves, allspice, and cinnamon sticks.
Pour in rum. Let steep in refrigerator for at least 1 week before using; quince may darken. Chill airtight up to 6 months; if liquid becomes cloudy, discard quince and spices.