Trinculo is one of many comic characters in Shakespeare, a jester who, along with the drunken servant Stephano, provides a foil to the pairings of Prospero and Alonso and Antonio and Sebastian. Most jesters in Shakespeare are actually quite intelligent, despite their professional foolery. (One thinks of Touchstone in As You Like It). But Trinculo most certainly isn't. He's a fool by nature as well as by profession.
As well as being incredibly stupid, Trinculo also has delusions of grandeur. He thinks he's so much better than he actually is, which is why he delights in lording it over Caliban, who's so desperate for someone to come along and rid him of Prospero that he literally licks Stephano's boots. Caliban wants to see Stephano take over as king of Prospero's island, and so does Trinculo, who sees a change of king as providing him with an opportunity to have a servant of his very own in the shape of Caliban.
But whereas Caliban's deadly serious about having Prospero killed, the increasingly absurd Trinculo and Stephano are much more concerned with the trappings of kingship, such as fancy gowns and servants. Indeed, Trinculo and Stephano's obsession with fine clothes ultimately thwarts their plan to overthrow Prospero. They are so engrossed by the flashy clothes left out from them by Ariel as a trap that they are easily chased away by a pack of magic spirit-hounds conjured up by Trinculo.