The departure follows on the heels of the agency recruiting Citizen Relations' Frankie Cory to replace Kaye as chief executive.
Kaye has previously described his hiring of Glover as creative director in 2006 as "the biggest career break I've had".
Glover became chairman of the agency in July when Kaye’s departure was announced. He said it was unlikely his chairman role would be filled, and identified Simon Moore, who joined as creative director in May, as a key part of a "strengthened creative team".
Glover told PRWeek that he had been thinking about leaving for some time, but wanted to assist with bringing in Kaye’s replacement.
"I have done seven years at Mischief and personally want a bit of a break to think about what I am doing next.
"The time is right for me to step away and think about what I want to do next, knowing Mischief is in the best possible shape it could be."
Mischief’s place within holding company Engine, which bought the agency in 2011, provided the "perfect model" for the agency to thrive, Glover claimed.
Pressed on whether he might be working with Kaye in the future, he responded: "I will not be thinking about my next steps until I finish what I am doing here."