Learn Icelandic: Fyrirlesturinn hefst eftir klukkutíma.

In Icelandic, to say that something will happen 'in' a certain amount of time from now, you use the preposition eftir (which usually means 'after'). You can think of it literally as 'after an hour has passed.'

What case does eftir force on the time word here?

When used to establish a future timeframe like this, eftir takes the accusative case. That is why we see klukkutíma, which is the accusative form of the weak masculine noun klukkutími.

Why does the verb hefst end in -st?

Hefst is the middle voice form of the verb hefja (to begin or raise). When an event like a lecture 'starts,' Icelandic uses this -st form to show it is happening on its own as a scheduled event, rather than saying a specific person is actively starting it.

Could I say byrjar instead of hefst?

Yes, byrjar (from the verb byrja) is very common and completely correct here. Hefst just sounds slightly more formal, which feels very natural when talking about an official event like a university lecture.