My recollection is that Kemp was the replacement for Richard Tarelton, and both were sort of song, dance, and slapstick type commedians. Kemp was replaced by Robert Armin, who was a more subtle type of commedian. He publish his jest book about different kinds of fools/jesters, 'Fool upon Fool' in 1600 and 1604 (both unique copies in Folger Shakespeare Library), and expanded it as 'A Nest of Ninnies' in 1608 (Folger and Bodleian). See his 'Derry's Fair' (Monaghan Fair), c 1597-9 in file BMADD on my website. Search on 'Tarleton' and 'Kemp' in the broadside ballad index on my website to turn up songs and tunes related to them.