Hello! Given that this question was asked last year, hopefully, you did not change your mind in pursuing this degree. I will answer your question in multiple parts so please excuse the long post. Keep in mind that this answer should not fully sway your decision in your career and academic path. Consider this a guidance.
1)The career choices with a Political Science degree (I am assuming a Bachelor's degree) from what I know can vary. From what I have seen in my academic career, those with a Political Science degree go into physical politics (run for local, county, state office), work with those along the campaign trail, or use their skills to analyze elements like voting behavior or election patterns (in this case they went further in their academic career to do so). I know there are others but this is just from what I have personally seen. To put plainly, a Bachelor's in Political Science may not be enough.
2) The most common plan I have seen is those with a Bachelor's in Political Science decide to go to law school. Keep in mind that you do NOT have to have a political science degree to get into law school, it can be any degree as long as it is a Bachelor's degree. There are those who graduate from law school who do not take the bar exam and attempt to find work in other fields. This can be a possible trajectory you can take if you want to go into the UN.
3) From what I can tell you, just with a Bachelor's in Political Science alone will NOT get you into the United Nations. I have a colleague who currently works at the UN. She was a journalist originally from Russia, who spoke English, Russian, and Spanish fluently. I met her when she was finishing up her Master's in Journalism. She was already working for a small news outlet. She interned at the UN FIRST and they applauded her fast work ethic so they hired her. What people do not tell you is that in order to try to work for the UN many decide to apply for the internship. I can tell you that it is extremely competitive and of course, you need the money/resources to not only go to their but also have enough to afford some sort of housing and feed yourself. I remember a friend of mine told me that a guy landed an internship at the UN and because he could not afford housing he lived in a tent. Make sure you have the proper resources before you decide to take this step.
4) From number 3, I think you understand my point that in order to work at a place like the UN, it is not just about your degree. It is also about your skills, knowledge, work ethic, and, other elements that make you unique. Once you finish your four-year degree, suddenly grades will NOT be the thing that matters anymore. It is truly about how to use your network and use your resources to your advantage.
5) So, if you want to work for the UN with a political science degree specializing in the Middle East, I believe that you should pursue a certificate as well. Many schools offer certificates specializing in a specific region or topic. It will be a lot of work on top of your degree but it can be rewarding. See if your school offers any certificates on the study of the Middle East or topics like Security or International Affairs.
6) Finally, I would like to encourage you to keep going in your studies. From what I have seen, a four-year degree is not enough anymore. If you can or if you want, pursue a higher education. Whether it is law school or a Master's degree I believe you can utilize your degree more if you get a higher education. First, you need to take the time in researching schools and really question whether this is something you want to do. Do NOT make a rash decision because that will be a waste of time, effort, and money. Whether it is law school or a Master's degree be ready to take either the LSAT or the GRE. So yes, more studying.
Good luck with your endeavors and I hope this answers your question.