Combine gin, elderflower liqueur, BeeMaid Honey simple syrup, and lime juice in a shaker filled with ice; shake well. Pour into a tall glass with ice and top with club soda.
Roll thyme sprigs between your hands a few times to release the oils and garnish with these and lime slices.
To make BeeMaid Honey simple syrup: Simmer ½ cup water, remove from heat and add 10 sprigs fresh thyme and two long strips lime peel removed with a vegetable peeler. Stir in ½ cup BeeMaid Honey until dissolved. Steep until cool; strain.