In a small saucepot, simmer the sugar in 1 cup of water until dissolved, about 3-4 minutes. Remove from heat and drop in the tea bags. Steep 10-12 minutes. Squeeze excess syrup from the used tea bags back into the pot and discard the bags.
In a shaker, combine the tequila, apple cider, 1/2 oz chai syrup (or more, to taste), lemon juice, and egg white. Dry shake for 30 seconds with no ice, then add ice and shake 30 seconds more until chilled. Strain into a coupe glass and garnish with a star anise, as desired.
Notes
*To store syrup: Unused syrup can be stored in the fridge, sealed, for up to 2 weeks.