The two-time Tony winner explores arts education at four Los Angeles organizations in the new special.
Composer Ingrid Michaelson also chats with host Clarkson about the new Broadway musical.
The song will be heard in Peacock's upcoming event series The Tattooist of Auschwitz.
Created, written, and narrated by Tony winner Buckley, The Mayfly is a love letter to music and New York City.
Da'Vine Joy Randolph and Halle Bailey are also in the cast, with Pharrell Williams producing.
Lissette Feliciano is set to write and direct.
The mononymic star is currently promoting her newest film Challengers, where she stars opposite Tony nominee Mike Faist.
Other Broadway names appearing in the festival's works include Trey Parker and Matt Stone, Rosie O'Donnell, Jesse Tyler Ferguson, and more.
Tony nominee O'Hara is set to direct the feature film adaptation of his comedy, which played The Public Theatre in 2015.