Not as a possessive determiner (before a noun).
For some reason, those inflect like the indefinite article ein and have no ending at all for masculine nominative, neuter nominative, and neuter accusative.
(As a possessive pronoun, replacing a noun, those endings would be correct. Dein Pferd is groß und unser(e)s ist klein; dein Hund ist schnell und unserer ist langsam. "Your horse is big and ours is small; your dog is fast and ours is slow." Even English has this distinction: no ending in possessive determiners, e.g. "our"; ending in possessive pronouns, e.g. "ours".)
Because attributive adjetives (roughly: ones before a noun) need an ending on them. You can't just put the base form neu before a noun like that.
Which ending depends on the gender, number, and case of the noun, as well as on whether you have a determiner in front of it and if so, what kind.
See e.g. https://en.wikipedia.org/wiki/German_adjectives for more information.
Here, you have neuter nominative singular, mixed inflection after possessive unser, and thus you need the ending -es on neues.