"The animal is young but big."
Translation:To zvíře je mladé, ale velké.
Because "zvíře" is neuter.
"Velký zvíře" is Common Czech, not standard Czech. It is a vernacular dialect or just a colloquial way to speak.
You could meet this colloquial form in a figurative meaning - "velký zvýře" is something like a "big boss".
You must tell your complete sentence. If you did then you are missing "To" and "je" for "the" and "is".
Well, in the grammar lessons it says: (Questioning 'To':) ''Czech doesn't have articles. Mladá dívka could be young girl, a young girl, or the young girl, depending on context.'' So if I say 'zvíře je mladé, ale velké', it is right too?
That would work in Russian, but not in Czech. Here you really do need the pronoun to signify it is THE animal. It is not always necessary, that's why the notes says what it says but most often it will be there.