هذه سنة جديدة.

Because سنة is a feminine noun, and the demonstrative this has to match it.

• هذا = this for masculine nouns
• هذه = this for feminine nouns

So:

• هذه سنة = this is a year
• not هذا سنة

Arabic requires this kind of gender agreement.

A very common clue is the ending ـة (called taa marbuuTa).

• سنة ends in ـة
• nouns with ـة are very often feminine

So سنة is feminine, which is why both the demonstrative and the adjective must also be feminine:

• هذه → feminine
• جديدة → feminine

Because adjectives in Arabic must agree with the noun they describe.

Here, جديدة describes سنة, so it matches it in:

• gender: feminine
• number: singular
• definiteness: indefinite

Compare:

• سنة جديدة = a new year / new year
• كتاب جديد = a new book

Since سنة is feminine, new becomes جديدة, not جديد.

In Arabic, descriptive adjectives usually come after the noun, not before it as in English.

So Arabic says:

• سنة جديدة literally: year new

But in natural English we translate it as:

• new year

This noun + adjective order is normal in Arabic.

In Arabic, the present tense of to be is often not stated.

So هذه سنة جديدة literally looks like:

• this year new

But it means:

• This is a new year

This is very common in Arabic nominal sentences. You do not need a separate word for is in the present tense.

Because the phrase is indefinite: a new year, not the new year.

• سنة جديدة = a new year
• السنة الجديدة = the new year

In Arabic, if the noun is definite with ال, the adjective also becomes definite:

• السنة الجديدة

If the noun is indefinite, the adjective stays indefinite too:

• سنة جديدة

In this exact form, it most naturally means:

• This is a new year

That is because هذه is functioning as the subject, and سنة جديدة is an indefinite predicate.

If you wanted this new year, you would usually say:

• هذه السنة الجديدة

So the presence or absence of ال changes the structure and meaning.

In Modern Standard Arabic, هذه is usually pronounced approximately as:

• haadhihi

A helpful breakdown:

• ها = haa
• ذِ = dhi
• final هِ = hi

So: haa-dhi-hi

In careful MSA pronunciation, all parts are heard. In less formal speech, you may hear reduced pronunciations, but for learning MSA, haadhihi is a good target.

سنة is pronounced approximately:

• sanah or sana(tun) in full grammatical reading

The final ـة (taa marbuuTa) is usually pronounced like -a / -ah when pausing.

So at the end of a sentence, learners commonly say:

• sanah

In full case-marked pronunciation, it can be:

• sanatun

But in normal unvocalized reading, you will often just hear sanah at pause.

Because it is the feminine form of the adjective new.

• masculine: جديد
• feminine: جديدة

Since it describes the feminine noun سنة, it must be feminine too.

So:

• كتاب جديد = a new book
• سنة جديدة = a new year

This is one of the most important agreement patterns in Arabic.

Yes. It is a very common Arabic sentence type called a nominal sentence.

It has two main parts:

• هذه = the topic / subject
• سنة جديدة = the predicate / what is being said about it

So the structure is:

• هذه
  • سنة جديدة
• This
  • a new year

This kind of sentence often has no written or spoken present-tense verb.

Yes. In fully vocalized, formal grammar, that is correct.

You may see:

• هذه سنةٌ جديدةٌ

Here:

• سنةٌ has -un
• جديدةٌ has -un

Those are nominative indefinite endings, because سنة جديدة is the predicate of the sentence.

In most everyday printed Arabic, these case endings are omitted, so you usually just see:

• هذه سنة جديدة

Both represent the same sentence; the second is simply the normal unvocalized writing style.

Normally, جديدة simply means new here, so the straightforward meaning is:

• This is a new year

However, like in many languages, context can affect nuance. Still, without extra context, a learner should understand it as a simple statement about a year being new. The grammar point to focus on is:

• feminine demonstrative: هذه
• feminine noun: سنة
• feminine adjective after the noun: جديدة