The Prime Minister is the bespectacled aide to King Goshposh in the Tales of the Tinkerdee pilot. His duties include taking inventory of Princess Gwendolinda's presents, and generally organizing things. He's only moderately more competent than the rest of the court, and tends to confuse his numbers when placing orders for cakes and sandwiches. In the later Tales from Muppetland specials, the Prime Minister would be replaced by Featherstone.
The Prime Minister's puppet began life as a nameless side character on Sam and Friends, sans glasses and with a nose. The puppet was reused in a variation of that form as the Scientist in the Pak-Nit industrial Shrinkenstein, and as Fred in the Kern's Bakery commercials.