Learn Hardcore Dutch: Mocht u te laat zijn, dan kunt u over een kwartier opnieuw binnenkomen. - If you should be late, then you can come in again in fifteen minutes.

It’s a formal conditional meaning “should (you)…/if (you happen to)…” rather than the past of mogen (“was allowed”). The pattern is: Mocht + subject + infinitive, (dan) + main clause. Neutral alternatives:

Als u te laat bent, …
Indien u te laat bent, … (formal)

Why is it zijn and not bent after u?

In the mocht-conditional, the lexical verb appears as an infinitive at the end: Mocht u te laat zijn. With als, you use the normal finite form: Als u te laat bent.

Is dan necessary? What does it do?

No, it’s optional. Dan corresponds to “then” in “if … then …” and improves flow: Mocht u te laat zijn, dan kunt u … Without it: Mocht u te laat zijn, kunt u … (also correct).

Why kunt u (verb before subject) instead of u kunt?

Dutch main clauses obey V2 word order: after any element in first position (here the whole conditional clause and/or dan), the finite verb comes next. Hence: …, (dan) kunt u …. In a standalone clause without something in front, you’d say U kunt ….

Does over een kwartier mean “in 15 minutes” or “after 15 minutes”? How is it different from na een kwartier?

over een kwartier = in 15 minutes from now.
na een kwartier = after 15 minutes have elapsed (often relative to some reference event). Don’t translate English “in 15 minutes” as in 15 minuten; in Dutch in 15 minuten means “within 15 minutes (duration).”

Why opnieuw and not weer or nog een keer?

All can mean “again.”

opnieuw: slightly more formal/neutral; “afresh/anew.”
weer: very common and casual “again.”
nog (een keer)/nogmaals: “once more.” In notices, opnieuw often sounds most neutral/formal, but weer would also be fine.

How does binnenkomen work here? Is it separable?

Yes, binnenkomen is separable.

With a modal, the verb stays together at the end: kunt u … binnenkomen.
Without a modal in a simple main clause, it separates: U komt (opnieuw) binnen.

Could I say te laat komen instead of te laat zijn?

Yes. Te laat komen focuses on the act of arriving late; te laat zijn is more state-like (“to be late”). Both are natural here.

What changes in the informal version with je/jij?

Mocht je te laat zijn, dan kun je/kan je over een kwartier weer naar binnen.
With als: Als je te laat bent, kun je/kan je … Both kun je and kan je are common; with jij (stressed), traditional grammar prefers jij kunt, but jij kan is widespread in speech.

Is u kan acceptable?

In the Netherlands, standard is u kunt. In Belgium (Flanders), u kan is common and accepted. For pan-Dutch formal writing, u kunt is the safest choice.

Should u be capitalized?

Modern standard spelling uses lowercase u. Capital U is an optional courtesy form in very formal letters; if you choose it, be consistent.

Are there other natural ways to phrase this conditional?

Yes:

Als u te laat bent, (dan) kunt u …
Indien u te laat bent, kunt u … (formal)
V1 conditional: Komt u te laat, dan kunt u … / Bent u te laat, dan kunt u …
Postposed conditional: U kunt over een kwartier opnieuw binnenkomen, mocht u te laat zijn.

How do you pronounce mocht?

The ch is a voiceless velar fricative (like German “Bach”): roughly “mokht.” The o is short, and the final t is pronounced.

Is te laat really “too late”? Could I use laat instead?

Te laat means “late relative to the agreed/expected time,” not necessarily “too late to be admitted.” Laat describes lateness in time of day or general lateness; for being late to an appointment, te laat (zijn/komen) is the idiomatic choice.

Do I need the comma?

Yes, place a comma after the fronted conditional: Mocht u te laat zijn, (dan) kunt u … After the comma, keep V2 (verb before subject). You can also append the mocht-clause at the end with a comma: U kunt …, mocht u te laat zijn.