Combine the pickle brine in a saucepan and boil on medium heat until the sugar dissolves (3 to 4 minutes). Stir occasionally. Remove from the heat and cool it down.
Place the julienned radishes and carrots into a sterile pickling jar and pour over the brine. Close the lid. Gently move the jar around a little bit to make sure the brine is touching the all radishes and carrots.
Leave the jar at room temperature for 3 to 4 hours then move to the fridge. Chill the pickles for 30 mins to 1 hour before serving for optimal taste.