Dacă promiteți că nu întârziați, vă aștept la recepție și continuăm lecția acolo.

Because they are 2nd person plural forms of the present tense, and Romanian also uses that same form for the polite singular you.

So promiteți can mean:

• you all promise, or
• you promise when speaking politely to one person

And întârziați can mean:

• you all are late / arrive late, or
• you are late / arrive late politely

In this sentence, the speaker is probably addressing one person politely, though it could also be more than one person.

Romanian usually drops subject pronouns because the verb ending already shows who the subject is.

So instead of saying:

• Dumneavoastră promiteți...
• Dumneavoastră întârziați...

Romanian normally just says:

• promiteți
• întârziați

The pronoun is only added for emphasis, contrast, or clarity.

Că means that.

So:

• promiteți că nu întârziați = you promise that you won’t be late

It introduces a subordinate clause, just like English that does.

Here a întârzia means to be late or to arrive late.

So:

• întârziați = you are late / you arrive late
• nu întârziați = you are not late / you do not arrive late

In natural English, this is often translated as:

• if you promise you won’t be late

Romanian simply puts nu before the verb to make it negative.

Vă is the unstressed pronoun meaning you:

• you polite singular, or
• you all

In vă aștept, it is the object of a aștepta:

• aștept = I wait
• vă aștept = I wait for you / I’ll be waiting for you

Romanian commonly uses these short object pronouns before the verb.

Because Romanian object clitic pronouns such as mă, te, îl, o, ne, vă, îi, le normally come before the conjugated verb.

So:

• vă aștept = correct
• aștept vă = not normal Romanian

This is a very common pattern:

• te văd = I see you
• vă chem = I call you
• îl cunosc = I know him

Romanian often uses the present tense for a future idea, especially when the future is understood from context.

In this sentence:

• vă aștept la recepție literally = I am waiting for you at reception
• but in context it means I’ll wait for you at reception
• continuăm lecția acolo literally = we continue the lesson there
• but naturally it means we’ll continue the lesson there

This is very normal in Romanian, especially:

• after dacă (if)
• when talking about planned or expected actions

English also sometimes does something similar:

• If you come on time, we continue there would be unnatural in English
• but If you come on time, we’ll continue there is the normal English translation

Dacă means if.

It introduces the condition:

• Dacă promiteți că nu întârziați... = If you promise that you won’t be late...

So the sentence structure is:

• condition: if you promise not to be late
• result: I’ll wait for you at reception and we’ll continue the lesson there

Because lecția means the lesson.

Romanian usually puts the definite article at the end of the noun, not as a separate word before it.

So:

• lecție = lesson
• lecția = the lesson

This is one of the most important features of Romanian grammar.

La recepție means at reception or at the reception desk/front desk.

Romanian often uses a noun without the definite article after prepositions when referring to a place in a general way.

So:

• la recepție = at reception
• la școală = at school
• la birou = at the office

If you wanted to make it more specifically definite, Romanian could say something like:

• la recepția hotelului = at the hotel’s reception/front desk

Because the action involves both the speaker and the listener: we continue the lesson together.

So:

• continuăm = we continue / we’ll continue

Even though the speaker is the one arranging things, the lesson is a shared activity, so we is the natural choice.

Yes, it sounds polite/formal because of promiteți, întârziați, and vă.

An informal singular version would be:

• Dacă promiți că nu întârzii, te aștept la recepție și continuăm lecția acolo.

Changes:

• promiteți → promiți
• întârziați → întârzii
• vă → te

But continuăm stays the same, because we continue still refers to both people together.