Under normally can't take an adjective. If a noun follows, under can act like an adjective (the under layer), and after a number it's an adverb (twelve and under). Neither is the is under + adjective pattern you asked about.
So don't write the coat is under new; write the coat is under the new pile. The noun pile, not the adjective, is what under points to.
When you're pointing at a layer or part: use the adjective before the noun
You're asking if an adjective can come right after is under. It can't in the pattern you're writing. Under points to a noun, so say the coat is under the new pile, where pile is the noun it takes.
You're describing a lower part directly before a noun. Then under itself works as an adjective: the under layer, the under surface of the leaf. That's a different position from your question, which is about what follows is under.
You're saying where something sits. If you name what it's below, give under a noun: the spot is under the leaf. If under truly stands alone as the adverb meaning below, that's a separate pattern, not an incomplete sentence to fix.
You want the adjective to carry the meaning. Put it before the noun and let under take that noun: not the coat is under new, but the coat is under the new pile. The noun, not the adjective, is what under points to.
You're writing about ages or amounts? That's covered separately below, where under trails the number as in twelve and under.
One contrasting check: the leaf is under can work as the adverb below, but if you mean below something specific, add the noun: the leaf is under the box.
If you're talking about an amount or age: under comes after the number
Ages and amounts flip the order: under follows the number, not the noun phrase. Say kids 12 and under or ten dollars and under. Here under works as an adverb meaning less or younger, so this isn't the preposition pattern taking an object.
Quick check: the coat is under new is never right, but twelve and under is fine. If a number comes first, let under trail it; otherwise give it a noun.