"This milk is new."
Translation:هٰذا الْحَليب جَديد.
The case you are talking about is the "attributive adjective" case. However in a predicative sentence where someone is telling a fact, the adjective and the noun before it do not mimic the same attributions, like being definite.
Here is an article which I hope it helps (done it 2 nights ago): https://forum.duolingo.com/comment/33483445
Well, the sentence here is out of context and the real meaning might not be inferred without a context.
For example, I personally would use this sentence if I was talking about a milk carton or box that has not been opened: Here we get boxes of milk packs (around 18 or 20 in each box can't remember and each pack is 1/4 liter), so I might use this sentence about a new (pack of) milk.
Another example maybe is when we check the date of production of the milk - I can say (new milk) about a milk which is the product of the day or the day before sort of (here they provide dairy products on almost a daily basis).
Maybe some people would use it for (fresh milk) as well, though I don't hear this often because most of the dairy products sold around here are packed and refrigerated. Usually (fresh milk) is dubbed as حليب طازج (Halíbun Tázaj) where the word (Tázaj) is borrowed from Farsi تازه but it is accepted in modern standard Arabic.