"My son will be a policeman."
Translation:Mój syn zostanie policjantem.
„Będzie” – yes, you can.
EDIT: Unless you wanted to say "I will be a policeman", then „Będę policjantem” is good.
to be = być
to become = zostać (zostawać)
I will be a policeman = Będę policjantem.
I will become a policeman = Zostanę policjantem.
The difference in meaning between these two words in Polish is fairly similar to that in English, so you can translate them directly.
How can you tell whether 'zostać' means 'to become' versus 'to stay' in a given context?
„Zostać” as in "to become" always comes with an object noun in instrumental case.
And what is the case that accompanies 'to stay'? Like if you were to stay a police officer? Thanks!
Ah, you meant that kind of "stay", when a person is already a policeman and will continue to do so? Then I would suggest using verbs like "pozostać", or "nadal być".