Combine the chopped celery, sugar and 2/3 cup water in a small saucepan. Bring to a simmer over medium heat and cook, stirring, until the sugar dissolves, 1 to 2 minutes. Let cool, about 30 minutes.
Strain the celery syrup into a pitcher and add the gin, lemon juice and tangerine juice. Pour into ice-filled glasses and top with seltzer. Garnish each with a lemon slice and some celery leaves.