"Yours is a new car" I have never seen or heard the use of "yours" like this before today, is this sentence grammatically correct?
The sentence is grammatically correct. The pronoun 'yours' can refer to something that comes before or after - this applies to 'yours' and the other strong (or absolute) possessive pronouns - yours is a new car; mine is the black dog; hers is a red bicycle; his is a big house; theirs are nice hats; ours was the victory; its was the red roof (of a house).
pronoun (PERSON/PEOPLE ADDRESSED)
the one(s) belonging to or connected with the person or group of people being spoken or written to:
Is this pen yours?
Unfortunately my legs aren't as long as yours.
I've got something of yours (= that belongs to you).
Yours is the room on the top floor, on the left.