Tibe is Estraven's political opponent. After Estraven is sent into exile, he succeeds as Prime Minister.
Perhaps the most telling aspect of Tibe is his mouth. The first and only time Ai actually meets Tibe, he can't stop noticing the Gethenian's teeth. Ai notes, "[Tibe] smiled again, and every tooth seemed to have a meaning, double, multiple, thirty-two different meanings" (1.29). Wow, that's, um, awkward but the double meanings certainly ring of political double speak.
But the trouble with Tibe's mouth doesn't end there. Although Ai never meets up with Tibe again, we hear from him from time to time over the radio. During his stint as prime minister, Tibe uses the radio to rally Karhide for war against Orgoreyn. He uses patriotic speeches "as praises of Karhide, disparagements of Orgoreyn, vilifications of 'disloyal factions,' discussions of the 'integrity of the Kingdom's border,' lectures in history and ethics and economics, all in a ranting, canting, emotional tone that went shrill with vituperation or adulation" (8.10).
Tibe, in other words, is basically the worst kind of politician. He uses a warped kind of patriotism to disguise the fact that all he's interested in is a power grab. At least King Argaven actually wanted to help out the whole country (or so he said)—Tibe is just out for himself.
This means Tibe's character conflicts with Ai's character. Ai wants to use open communication with the Ekumen to promote peace and the growth of culture while Tibe wants to use communication to bolster his power by starting a war. Jeez, wonder who we're supposed to root for in this scenario?