"László is not an engineer, but a policeman."
Translation:László nem mérnök, hanem rendőr.
My Hungarian teacher taught it as "nincs" = "nem van" also, because nem van is never said. Try to think of it as the negative third person singular form of the verb "to be". I walked into a store and asked for a pineapple and the lady said "nincs" ("there is none"- they didn't have pineapples at that store). "Nincs házam" doesn't have a literal English translation that's grammatically correct, but it would be something like "there is no house of mine".
Don't I need a verb in this sentence? Or isn't a verb at least optional?
No offense, I'm unironically wondering how you have made it till this chapter without understanding or at least encountering "zero copula" in third person ie. the drop of "van" and "vannak" when their only purpose is to connect a noun or a pronoun to another noun or adjective.
This was the main topic of Basic 1 actually https://www.duolingo.com/skill/hu/Basic-1/tips-and-notes