What is the main conflict in this novel and how does it get resolved?
There are quite a number of conflicts in the novel; for example, the various revolutions, Shevek's feelings of guilt at attaining so privileged a position at the Institute, the dichotomous societies on Urras, the use of technology for war or peace, and the implied conflict between whether the society on Urras or Anarres is the better one (calling Anarres an "ambiguous utopia" makes it clear that it is not objectively superior).
I would argue that the "main" conflict is Shevek's work; he spends the majority of the novel trying to get his Simultaneity project completed, resulting in the development of the ansible at the end of the story. Out of all the conflicts, this is the only one that is truly resolved; Shevek isn't really a part of either society at this point, but his perseverance allows him to see and overcome the strengths and weaknesses of both, resulting in something that is good for everyone.
Thus, I think you could say that the primary conflict is that of the individual versus society, and that it is resolved symbolically in the development of the ansible, which shows that the individual has the power to remake society.