Learn Hardcore Turkish: Defter eski, yenisini istiyorum. - The notebook is old; I want the new one.

yeni = new
-si = 3rd‑person possessive used here to turn the adjective into a noun-like word: yenisi = the new one
-n(i) = accusative case (with buffer n after a possessive): yenisini = the new one (as a specific direct object)

The -si doesn’t indicate real ownership; it’s a common way to substantivize adjectives in Turkish.

Why is yenisini in the accusative case?

Because istemek (to want) takes the accusative when the object is specific/definite. Yenisini istiyorum means I want the new one (a specific thing understood from context). If you mean an indefinite item, you’d say yeni bir defter istiyorum (I want a new notebook), which has no accusative on the object.

Can I just say yeni istiyorum?

Not by itself. Yeni is an adjective; you either:

name the noun: yeni bir defter istiyorum (I want a new notebook), or
turn the adjective into a noun-like form: yenisini istiyorum (I want the new one), or
use a generic one: yeni bir tane istiyorum (I want a new one), or
say it more explicitly: yeni olanını istiyorum (I want the one that is new).

What does the comma do in Defter eski, yenisini istiyorum? Could I use çünkü?

The comma separates two simple clauses and implies a reason/contrast: The notebook is old, so I want a new one. You can make the link explicit:

Defter eski, bu yüzden yenisini istiyorum.
Defter eski olduğu için yenisini istiyorum.
Defter eski, o yüzden yenisini istiyorum.

Why is there no verb meaning is in Defter eski?

Turkish uses a zero copula in the simple present for nominal sentences. Defter eski corresponds to The notebook is old. For variations:

Negative: Defter eski değil.
Question: Defter eski mi?
More formal/assertive: Defter eskidir.

What nuance does -dir add in Defter eskidir?

The suffix -dir adds formality, general truth, or inference (it can sound like you’re concluding or stating a known fact). In everyday speech, people usually just say Defter eski.

Why istiyorum and not isterim?

istiyorum (present continuous) is the normal way to express a current desire: I want (now).
isterim (aorist) tends to express general preference/habit or a polite, somewhat detached offer/request. In a restaurant you’ll typically say … istiyorum, not … isterim.

Does the -si in yenisi mean its, like possession? Is there gender?

It’s the 3rd‑person possessive form, but here it functions mainly as a pronominalizer, turning an adjective into something like the one that is new. Turkish has no grammatical gender; -si is not gendered.

How would I say it with a plural noun: The notebooks are old; I want new ones?

Defterler eski, yenilerini istiyorum. Here yenilerini = yeni-ler-i-n(i) (new + plural + pronominalizer + accusative). It means the new ones (of them), again referring back to the understood set of notebooks.

Can I add a pronoun like onun or onu?

Onun yenisini istiyorum = I want its new one (explicitly linking to a previously mentioned item).
Onu istiyorum = I want it (no mention of new).
In your sentence, Yenisini istiyorum already encodes the idea of new one tied to the context.

Can I drop the accusative and say yenisi istiyorum?

It’s best not to. Since you mean a specific, identifiable object, standard Turkish marks it with the accusative: yenisini istiyorum. If you mean an indefinite item, switch to yeni bir defter istiyorum or yeni bir tane istiyorum.

How is yenisini pronounced, and what are the buffer letters?

Syllables: ye-ni-si-ni.
Buffers: s appears between a vowel-final stem (yeni) and the possessive -i → yeni-si; n appears between the possessive and a case ending → yenisi-ni.
Vowel harmony gives the final -i (front vowel) here.
Main stress in finite verbs is typically on the last syllable: istiyorúm; the words defter and eski carry normal Turkish word-final stress patterns.

Is there a more explicit way to say the one that is new?

Yes: yeni olanını istiyorum literally the one that is new (accusative). It’s a bit more formal/emphatic than yenisini.