Tandlægevagten er åben; klinikken kan flytte tiden eller aflyse tiden.

Because Danish, like English, often makes compound nouns, but Danish usually writes them as one word.

• tandlæge = dentist
• vagt = duty / emergency service / on-call service
• tandlægevagt = dental emergency service
• tandlægevagten = the dental emergency service

So Tandlægevagten is not unusual at all in Danish. Long compound words are very common.

The ending -en is the definite article attached to the noun. In English, Danish often says the by adding it to the end of the word.

So:

• en tandlægevagt = a dental emergency service
• tandlægevagten = the dental emergency service

This is a very important Danish pattern.

Because åben agrees with the grammatical gender/number of the noun it describes.

Here, tandlægevagten is a common-gender singular noun, so the adjective is:

• åben = open

Compare:

• klinikken er åben = the clinic is open
• huset er åbent = the house is open
  (because hus is neuter)
• klinikkerne er åbne = the clinics are open
  (plural)

So åben is correct because tandlægevagten is singular and common gender.

Literally, yes: tiden means the time. But in medical, dental, and service contexts, tid often means appointment.

So in this sentence:

• flytte tiden = move/reschedule the appointment
• aflyse tiden = cancel the appointment

This is very common Danish usage. A native English speaker may expect a word more like appointment, but Danish often uses tid in exactly this way.

The sentence says:

• flytte tiden eller aflyse tiden

Danish could also say:

• flytte eller aflyse tiden

Both are understandable. Repeating tiden makes the sentence a little clearer and slightly more formal or explicit, especially in notices or informational writing.

So the repetition is not wrong; it is just a stylistic choice.

Yes, in some contexts you could replace the second tiden with den:

• klinikken kan flytte tiden eller aflyse den

That is grammatical. But repeating the noun can sound clearer in official or practical messages. Danish often prefers repeating a noun when there is any chance of ambiguity.

This is a modal verb structure.

• kan = can / may / is able to
• flytte = move
• aflyse = cancel

After a modal verb like kan, the next verb stays in the infinitive form:

• kan flytte
• kan aflyse

This is similar to English:

• can move
• can cancel

So the pattern is straightforward: subject + kan + infinitive

The semicolon links two closely related independent clauses:

• Tandlægevagten er åben
• klinikken kan flytte tiden eller aflyse tiden

A semicolon is stronger than a comma and weaker than a full stop. It shows that the two ideas belong together.

You could also write this as two sentences:

• Tandlægevagten er åben. Klinikken kan flytte tiden eller aflyse tiden.

The semicolon is just a punctuation choice.

Klinikken means the clinic.

• en klinik = a clinic
• klinikken = the clinic

Danish often uses the definite form when the thing is already known from the context. In a notice like this, it is understood that a specific clinic is being referred to, so klinikken is natural.

Yes. Aflyse is the standard everyday verb for canceling appointments, meetings, events, and similar plans.

Examples:

• aflyse en tid = cancel an appointment
• aflyse et møde = cancel a meeting
• aflyse en koncert = cancel a concert

So aflyse tiden is very natural Danish.

No, Danish nouns are not normally capitalized. Tandlægevagten has a capital T only because it is the first word of the sentence.

So inside a sentence, it would normally be:

• tandlægevagten

This is different from German, where all nouns are capitalized.

In theory, yes, because tid literally means time. But in real-life context, especially with a clinic, a native speaker will normally understand tiden as the appointment time or simply the appointment.

So the context does the work here. In healthcare and booking contexts, tid very often means appointment.