Add the gin, Cucumber-Thyme Juice and 1 sprig thyme to a shaker with ice and shake until well combined. Strain into a glass with ice, pour in the tonic and stir. Garnish with a slice of cucumber and a sprig of thyme.
Puree the thyme and cucumber in a food processor until smooth, about 40 seconds. Place a sieve on top of a bowl and strain the juice from the pulp.