Learn Farsi: این خانه‌ی جدید کوچک نیست اما بزرگ است. - This new house is not small, but it is big.

نیست (nist) is the 3rd-person singular form of the negative "to be" verb (meaning "is not"). We use it because the subject of the sentence, این خانه‌ی جدید (this new house), acts as an "it".

Why is there a ی attached to the end of خانه (house)?

This is the ezāfe connecting the noun to its adjective. In Farsi, adjectives come after the noun they describe, linked by an "e" or "ye" sound. Because خانه (khāne) ends in a vowel, we use ی (ye) to smoothly connect it to جدید (jadid / new), making it خانه‌ی جدید (khāne-ye jadid).

Does the negative verb always go after the adjective, like نیست (nist) does here?

Yes! Farsi puts the verb at the very end of the clause. That is why "is not small" is built as کوچک نیست (small is-not). When the sentence continues with اما (ammā / but), a new clause starts, so the positive verb است (ast / is) also goes at the very end.

Why doesn't the second half of the sentence use a word for "it" before بزرگ (big)?

In Farsi, you can drop the subject pronoun (like "it") if it is already obvious from the first half of the sentence. بزرگ است (bozorg ast) just means "big is", but because we are still talking about the house, the "it" is completely understood.