new: recently made or come into being, or fresh and never seen before
This is the ordinary Hebrew word for new, and it covers the same ground the English word does. It can simply mean recently produced: a cart that has never been used, a house just built, a garment off the loom, ropes that have not yet frayed. It can also mean fresh in a deeper sense, something that has never existed or been experienced before, which is why the Bible reaches for it to describe a new song, a new heart, a new covenant, and a new heaven and a new earth.
The two shades are not different words but two ends of one idea. At the plain end, new marks an object as recent and unused, often because that matters for the story (a brand new cart and a brand new bowl are fit for sacred use; new ropes should have held a strong man). At the fuller end, new carries the weight of the unprecedented, what God is about to do that has no parallel in what came before.
The same word lies behind the famous line that there is nothing new under the sun. There the point is the opposite of the promises: human life keeps repeating itself, and no genuinely fresh thing appears. The contrast only works because the word can mean truly unprecedented, which is exactly what the prophets claim God will bring.