Tandlægevagten er åben i aften; jeg må kontakte tandlægevagten.

Because Danish, like German, very often makes compound nouns by joining smaller words together.

Here, tandlægevagten is built from:

• tand = tooth
• læge = doctor
• vagt = on-call service / emergency duty

So tandlægevagt is the dental emergency service or emergency dentist service.

Then the ending -en is added to make it definite:

• tandlægevagt = an emergency dental service
• tandlægevagten = the emergency dental service / the emergency dentist on duty

This is completely normal in Danish: one idea is often written as one word.

The ending -en is the definite article attached to the noun. Danish usually puts the at the end of the noun instead of as a separate word.

Compare:

• en tandlægevagt = an emergency dentist service
• tandlægevagten = the emergency dentist service

This is one of the biggest differences from English. Instead of saying a separate word like the, Danish often uses a suffix:

• bil = car
• bilen = the car

So tandlægevagten already includes the meaning of the.

Danish can repeat the noun for clarity, especially in short formal or practical sentences.

So:

• jeg må kontakte tandlægevagten = I have to contact the emergency dentist service

It would also be possible in some contexts to refer back with a pronoun, but repeating the noun is often clearer and very natural, especially when talking about services, offices, or institutions.

The repetition makes the sentence sound direct and unambiguous.

Because åben agrees with the grammatical gender and form of the noun it describes.

Here, tandlægevagten is based on vagt, which is a common gender noun. With a common gender singular noun, the adjective is often in its basic form:

• Vagten er åben = The service is open

You often see åbent with neuter nouns:

• Huset er åbent = The house is open

So:

• common gender singular: åben
• neuter singular: åbent

I aften means this evening / tonight.

In Danish, time expressions often use prepositions differently from English. Here:

• i can mean something like in or be part of a fixed time phrase
• aften = evening

Together, i aften is just the normal way to say tonight / this evening.

Other similar expressions are:

• i dag = today
• i morgen = tomorrow
• i nat = tonight / at night

So you should learn i aften as a set phrase.

Here må expresses necessity/obligation, so it means something like:

• must
• have to
• need to

So jeg må kontakte tandlægevagten means I must / have to contact the emergency dentist service.

This verb can sometimes also express permission, depending on context:

• Du må gå nu can mean You may go now

But in your sentence, the context clearly points to necessity, not permission.

Sometimes, but the nuance changes.

• må often suggests necessity, sometimes because of the situation
• skal often suggests something is required, planned, or expected

So:

• Jeg må kontakte tandlægevagten = I have to contact the emergency dentist service
• Jeg skal kontakte tandlægevagten = I am supposed to / I will need to contact the emergency dentist service

In many real situations, both might be possible, but må often sounds more like I really need to because of the circumstances.

This is normal Danish main-clause word order.

In a simple statement, Danish usually follows this pattern:

• subject + finite verb + other verbs/complements

So:

• jeg = subject
• må = finite verb
• kontakte = infinitive/main verb

That gives:

• jeg må kontakte tandlægevagten

This is similar to English:

• I must contact the emergency dentist service

Because after a modal verb like må, Danish uses the bare infinitive.

So you say:

• jeg må kontakte not
• jeg må at kontakte

This is similar to English:

• I must contact not
• I must to contact

Other common modal verbs that work the same way include:

• kan = can
• vil = will / want to
• skal = shall / must
• bør = ought to

Examples:

• Jeg kan komme = I can come
• Jeg vil spise = I want to eat
• Jeg skal arbejde = I have to work

The semicolon links two closely related independent clauses:

• Tandlægevagten er åben i aften
• jeg må kontakte tandlægevagten

Each part could stand as its own sentence, but the semicolon shows a strong connection between them. The second clause follows logically from the first.

It is similar to writing:

• The emergency dentist is open tonight; I have to contact them.

In everyday Danish, many people would also just use a full stop or sometimes a comma, depending on style.

Because Danish does not capitalize all nouns.

Unlike German, Danish only capitalizes:

• the first word of a sentence
• proper names
• certain special cases

So tandlægevagten is lowercase unless it begins a sentence, as it does here:

• Tandlægevagten er åben i aften

If the same word appeared in the middle of a sentence, it would normally be lowercase:

• Jeg må kontakte tandlægevagten

It can function as either, depending on context, but most often it refers to the service/clinic/on-call emergency dental service as an institution.

So in this sentence, a learner should probably understand it as:

• the emergency dentist service
• the on-call dental emergency clinic

When you say kontakte tandlægevagten, you are usually contacting the service, not necessarily one specific dentist personally.

Læge means doctor in general, while tandlæge specifically means dentist.

The word tandlæge is itself a compound:

• tand = tooth
• læge = doctor

So literally it is a tooth doctor, which is exactly what a dentist is.

This is a very common and useful Danish word to remember:

• en læge = a doctor
• en tandlæge = a dentist

The given sentence is perfectly understandable, but in everyday speech a Dane might also say something a little more conversational, for example:

• Tandlægevagten har åbent i aften, så jeg må kontakte dem.
• Tandlægevagten er åben i aften, så jeg må kontakte dem.

A few notes:

• har åbent is a very common way to say is open
• så = so
• dem = them

Your original sentence is still correct; these are just more conversational alternatives.