"It is a new department in the university."
Translation:Це новий факультет в університеті.
"Faculty" often means a teaching body (professors, teaching assistants etc). So "факультет" is best translated as "department"
So "факультет" is best translated as "department"
ok, and what is the best translation for "кафедра"?
Depends on the context, which country you're talking about, and what you actually mean by "кафедра":
1) If you mean "teachers/lecturers" as in "Вчора кафедра обговорювала навчальний план", then you could use "The faculty was/were discussing the curriculum yesterday".
2) If you mean a sub-department, then it could be "chair". In Germany, where I've been studying, professors had their own "chairs", and such a chair consisted of a professor, 3-4 assistant professors, and around 10 research assistants. Like, for example, "Chair of Strategic and International Management". These people were teaching a set of related courses, pretty much like "кафедри" in Ukraine. I think this is the most direct translation.
3) Finally, if you're talking about a Business School, for example, (which may at the same time be a separate university), then the largest units within such a school will likely be called departments, as you suggested. Like "The Department of Finance at Copenhagen Business School".
There might be other conventions in the US. Here I tried to describe my experience for Europe. So, I don't think there is one correct translation of Ukrainian "кафедра" which would be understood by all English-speakers in the same way. The chioce would depend on whom you're talking to, and which message you want to carry. Hope this helps :)