Remove leaves from 1 thyme sprig; place in cocktail shaker. Add 6 berries; mash with muddler or wooden spoon. Fill cocktail shaker with ice; add gin, Simple Syrup, and lime juice. Cover; shake vigorously until cold. Strain into highball glass filled with ice. Thread 1 raspberry onto remaining thyme sprig; place on rim of glass.
Stir 1 cup sugar and 1 cup water in small saucepan over low heat until sugar dissolves. Bring to boil; cool. Cover and chill.