Combine the sugar, water, lemon juice and zest in a small saucepan and bring to a boil, stirring occasionally. Add the rhubarb and the tarragon, reduce the heat and simmer on low heat for 5  minutes.

Remove from heat and let stand until cool, about 20 minutes. Remove the tarragon sprig.

You may strain the chunks of rhubarb out of the syrup if you do not want the pulp. Otherwise, leave the rhubarb for a stronger rhubarb flavor.

Pour the syrup into a resealable jar or container and store in the refrigerator for up to 1 week.