In a small saucepan, combine the apple cider vinegar, water, sugar, salt, and dry mustard. Bring the mixture to a boil, stirring until the sugar dissolves.

Pack the beet slices into a clean jar and pour the hot brine over them, ensuring they are fully submerged.

Let the jar cool to room temperature (about 2 hours), then seal it with a tight lid and place it in the refrigerator. Allow the beets to pickle for at least 24 hours before serving.