Combine the water and sugar in a small saucepan. Stir over low heat until sugar dissolves. Turn off the heat and let cool to room temperature.
In a bowl or cup with a spout, combine the ginger beer, simple syrup and lime juice.
Place a slice or two of the apple in each popsicle mold and pour in the ginger beer mixture. Leave at least ¼ inch headroom for expansion. Add the sticks.
Freeze for at least 4 hours.
Notes
This recipe will fill 8 - ⅓ cup popsicle molds. Can substitute ½ cup of honey for the sugar.