طبيب الأسنان في العيادة.

Because طبيب الأسنان is an iḍāfa construction, often called a genitive construction.

In an iḍāfa:

• the first noun does not take الـ
• the whole phrase gets its definiteness from the last noun

So:

• طبيب أسنان = a dentist
• طبيب الأسنان = the dentist

Here, الأسنان is definite because it has الـ, so the whole phrase طبيب الأسنان becomes definite: the dentist.

Also, the first noun in iḍāfa does not take tanwīn either.

That is simply the normal Arabic way to express this profession in Modern Standard Arabic.

• طبيب = doctor
• الأسنان = the teeth

So طبيب الأسنان literally means doctor of the teeth, but naturally it means dentist.

Many Arabic job titles work this way, using an iḍāfa:

• مدرس اللغة العربية = teacher of the Arabic language
• مدير المدرسة = principal/director of the school

So this structure is very common and natural.

Because Arabic normally uses teeth in this expression: طبيب الأسنان.

English says dentist, which does not visibly contain the word teeth, but Arabic builds the idea as doctor of the teeth. Using the plural is the standard expression.

A singular form like طبيب السن would not be the normal general word for dentist.

In Arabic, the present-tense verb to be is usually not stated in simple nominal sentences.

So:

• طبيب الأسنان في العيادة
  literally: the dentist in the clinic
• natural English: The dentist is in the clinic

Arabic often leaves out is / am / are in the present tense.

Compare:

• الولد طويل = The boy is tall
• أنا متعب = I am tired
• طبيب الأسنان في العيادة = The dentist is in the clinic

If you want past tense, then Arabic does use a verb:

• كان طبيب الأسنان في العيادة = The dentist was in the clinic

It is most naturally understood as a full nominal sentence:

• طبيب الأسنان = the subject
• في العيادة = the predicate, meaning in the clinic

So the sentence means The dentist is in the clinic.

However, without context, Arabic strings like this can sometimes also function as a noun phrase, depending on how they are used. For example, in a larger sentence, it could mean something like the dentist in the clinic.

But standing alone with a period, learners should usually read it as a complete sentence.

It is a nominal sentence in Modern Standard Arabic.

Its parts are:

• طبيب الأسنان = mubtadaʾ (subject/topic)
• في العيادة = khabar (predicate/comment)

Inside طبيب الأسنان, there is also an iḍāfa:

• طبيب = first term of the iḍāfa
• الأسنان = second term of the iḍāfa

And inside في العيادة:

• في = preposition
• العيادة = noun governed by the preposition

So the structure is basically:

[The dentist] [is in the clinic].

في is the preposition meaning in.

So:

• في العيادة = in the clinic

After a preposition like في, the following noun is in the genitive case.

That is why, in fully vocalized Arabic, it would be:

• فِي الْعِيَادَةِ

The final -i sound reflects the genitive case.

In fully vocalized MSA, it would be:

طَبِيبُ الْأَسْنَانِ فِي الْعِيَادَةِ

Case by case:

• طبيبُ = nominative, because it is the subject of the nominal sentence
• الأسنانِ = genitive, because it is the second part of the iḍāfa
• العيادةِ = genitive, because it comes after في

In normal unvocalized writing, these endings are usually not written, and in pause they are often not pronounced fully.

A careful pronunciation is:

ṭabību l-asnāni fī l-ʿiyādati

A few useful notes:

• ط is an emphatic t
• ذ is not here; الأسنان has س, a normal s
• ع in العيادة is a consonant that English does not have
• in connected speech, the a of al- often drops after the previous word, so you hear ṭabību l-asnān, not a full separate al

If you pause naturally at the end, learners often say something closer to:

ṭabīb al-asnān fī al-ʿiyāda

That is a useful learner-friendly pronunciation.

You would normally make the iḍāfa indefinite:

• طبيب أسنان = a dentist

Compare:

• طبيب الأسنان = the dentist
• طبيب أسنان = a dentist

The key difference is whether the second noun is definite or indefinite.

But remember: when this phrase is used as the subject of a full sentence, Arabic handles indefiniteness a bit differently than English, so sentence patterns may change depending on context.

In Modern Standard Arabic, طبيب الأسنان is the standard and safest form for dentist.

• طبيب is the standard MSA word for doctor/physician
• دكتور is also common in real life, but it can mean doctor in a broader sense, including someone with a doctorate

In everyday speech, many people do say دكتور الأسنان, and native speakers would understand it. But for formal MSA learning, طبيب الأسنان is the better choice.