Bring the carrots, water, sugar and salt to a gentle boil and simmer in a small saucepan for 10 minutes. Stir occasionally.
Remove the pan from the heat and add in the tarragon. Stir and allow to steep and cool for 10 minutes more.
Strain and then add in the apple cider vinegar. Cool completely and serve over ice with an ounce of vodka or gin and splash of procecco.
Or for a non-alcoholic experience. Fill a glass with ice, fill it with half carrot shrub and half sparkling water.