Έχει καινούριο τατουάζ.

Έχει is the 3rd person singular, present tense of έχω = to have.

So:

• έχω = I have
• έχεις = you have
• έχει = he/she/it has

In this sentence, έχει means has.

Greek often leaves out subject pronouns when the verb already shows who the subject is. This is very normal.

So Έχει καινούριο τατουάζ. naturally means:

• He has a new tattoo
• She has a new tattoo

If you want to make the subject explicit, you can add:

• Αυτός έχει καινούριο τατουάζ. = He has a new tattoo
• Αυτή έχει καινούριο τατουάζ. = She has a new tattoo

Usually, though, Greek does not need the pronoun unless you want emphasis or contrast.

Καινούριο is the neuter singular form of the adjective καινούριος / καινούρια / καινούριο = new.

It has to agree with τατουάζ, which is treated as a neuter noun in Greek.

So the agreement is:

• masculine: καινούριος
• feminine: καινούρια
• neuter: καινούριο

Because τατουάζ is neuter, Greek uses καινούριο.

Τατουάζ is a neuter noun in Greek.

It is also an indeclinable loanword, which means its form usually stays the same. So you do not see the usual ending changes that many Greek nouns have.

That is why the adjective tells you a lot:

• καινούριο τατουάζ = singular neuter
• καινούρια τατουάζ = plural neuter

It is the direct object of έχει, so it is in the accusative.

However, with many neuter singular nouns and adjectives in Greek, the nominative and accusative forms are the same. So even though it is accusative here, it looks the same as the dictionary-style form.

Yes, you absolutely can say Έχει ένα καινούριο τατουάζ.

Both are natural:

• Έχει καινούριο τατουάζ.
• Έχει ένα καινούριο τατουάζ.

Greek often omits the indefinite article ένα in this kind of sentence, especially in everyday speech, when talking about what someone has.

The version without ένα can sound a bit more natural or streamlined in casual Greek.
The version with ένα is also correct and may feel slightly more explicit.

Yes, Greek word order is more flexible than English word order.

The most neutral version here is:

• Έχει καινούριο τατουάζ.

You can move words around for emphasis, but the tone changes. For example:

• Καινούριο τατουάζ έχει. = emphasis on new tattoo
• Τατουάζ έχει. = emphasis on the fact that there is a tattoo

For a learner, the safest default is:

• verb + adjective + noun here: Έχει καινούριο τατουάζ.

A rough pronunciation is:

EH-khee keh-NOO-ree-oh tah-too-AHZ

More accurately:

• Έχει = /ˈeçi/
• καινούριο = /ceˈnuɾio/
• τατουάζ = /tatuˈaz/

The accent marks show which syllable is stressed:

• Έχει
• καινούριο
• τατουάζ

So the stress falls on:

• first syllable of Έχει
• νού in καινούριο
• last syllable of τατουάζ

Yes. Both are common and correct:

• καινούριο τατουάζ
• καινούργιο τατουάζ

They both mean new tattoo.
In everyday Greek, you will hear both forms.

Yes, νέο τατουάζ is possible.

But there is a slight nuance:

• καινούριο often feels like newly acquired / brand new
• νέο can also mean new, but may sound a little more general or slightly more formal depending on context

In everyday speech, καινούριο τατουάζ is very natural for a new tattoo.