Something chewed over

CUD

["Consider what a horse might hold in its mouth while being ridden."]

The clue "Something chewed over" hints at "cud," which is a piece of food, like hay or sugar, given to horses to chew on. It also plays on the phrase "chew the cud," meaning to think deeply or ponder something. The word "cud" fits both the literal and figurative meanings of the clue.