Hvis hendes cv er klart i aften, tror hun, at hun snart bliver ansat.

Because Danish main clauses follow the V2 rule: the finite verb must come in the second position.

Here, the whole clause Hvis hendes cv er klart i aften comes first. That means the verb of the main clause must come next:

• Hvis hendes cv er klart i aften, tror hun ...

If there were no fronted Hvis-clause, the normal order would be:

• Hun tror, at hun snart bliver ansat.

So this is a very common Danish word-order pattern.

Hvis is used for a real condition, like English if.

So Hvis ... means if ...

A common learner confusion is with om. Danish om can mean whether/if in indirect questions, but not this kind of condition.

Compare:

• Hvis hendes cv er klart ... = a condition
• Hun ved ikke, om hendes cv er klart. = she does not know whether her CV is ready

Because sin/sit/sine can only refer back to the subject of the same clause.

In the clause Hvis hendes cv er klart i aften, the subject is hendes cv, not hun. So Danish does not use sit here.

That is why hendes is correct.

Compare:

• Hun sender sit cv.
  Here hun is the subject of the same clause, so sit is possible.

• Hvis hendes cv er klart ...
  Here hun is not the subject of that clause, so hendes is used.

Because cv is a neuter noun in Danish: et cv.

When an adjective matches a singular neuter noun, it usually takes -t:

• en rapport er klar
• et cv er klart

So klart agrees with cv.

Because at introduces a subordinate content clause, similar to English that.

After verbs like tro, vide, sige, and mene, Danish often uses at before the clause that follows:

• Hun tror, at hun snart bliver ansat.

In everyday speech, at is sometimes omitted, but in normal written Danish it is very common to keep it.

Bliver ansat focuses on the event of getting hired.

Er ansat describes the state of already being employed.

So the difference is roughly:

• bliver ansat = gets hired / is hired
• er ansat = is employed

Here the sentence is about what she thinks will happen soon, so bliver ansat fits better.

Danish often uses the present tense to talk about the future, especially when a time expression makes it clear.

In this sentence, the future idea is shown by:

• i aften
• snart

So Danish does not need a separate word like English will here.

This is very normal:

• Vi ses i morgen.
• Hun kommer snart.
• Hun bliver snart ansat.

I aften is the normal Danish expression for this evening / tonight.

Danish often uses i with fixed time expressions like this:

• i dag
• i morgen
• i aften

So i aften is just the natural idiomatic form.

Because Danish uses commas to mark subordinate clauses.

In this sentence there are two subordinate clauses:

• Hvis hendes cv er klart i aften
• at hun snart bliver ansat

So the commas help show where those clauses begin or end:

• after the initial Hvis-clause
• before the at-clause

This punctuation is very typical in written Danish.