Wij lichten Tom in; daarna duikt hij op.

Because both are separable verbs in Dutch.

• inlichten = inform
• opduiken = show up / appear / turn up

In a main clause, Dutch usually puts the finite verb in second position, and the separable prefix moves to the end:

• Wij lichten Tom in.
• Hij duikt op.

So the full verbs are:

• inlichten
• opduiken

But in this sentence they appear as:

• lichten ... in
• duikt ... op

This is very common in Dutch.

Because in a normal Dutch main clause, the conjugated verb must come early, usually in second position.

So Dutch does this:

• subject: Wij
• finite verb: lichten
• object: Tom
• separable prefix: in

That gives:

• Wij lichten Tom in.

Putting inlichten together in a main clause would sound wrong.

You only keep it together in places like the infinitive or participle:

• We moeten Tom inlichten.
• We hebben Tom ingelicht.

That is normal with separable verbs. The prefix goes to the end of the clause, and other sentence parts stay in the middle.

So:

• Wij lichten Tom in. = We inform Tom.

Here:

• lichten = verb part
• Tom = object
• in = separable prefix

You can think of it as the clause “holding open” a slot for the prefix at the end.

Iemand inlichten means to inform someone, to brief someone, or to let someone know.

So:

• Wij lichten Tom in = We inform Tom

It is a bit more formal or purposeful than just zeggen (to say/tell).

A common pattern is:

• iemand inlichten over ...
• iemand ergens over inlichten

For example:

• We lichten Tom in over het plan. = We inform Tom about the plan.

In your sentence, the topic is simply not stated.

Opduiken means to appear, to show up, to turn up, sometimes with a slight sense of suddenly or unexpectedly.

So:

• daarna duikt hij op = after that he shows up / turns up

Depending on context, opduiken can feel a bit more vivid than a plain verb like verschijnen.

It can also be used for things, not just people:

• Er dook een probleem op. = A problem came up.

Because Dutch main clauses follow the verb-second rule.

If daarna comes first, then the finite verb must come immediately after it:

• Daarna duikt hij op.

Structure:

• first position: daarna
• second position: duikt
• subject: hij
• separable prefix: op

So when something other than the subject comes first, the subject usually moves after the verb.

Compare:

• Hij duikt daarna op.
• Daarna duikt hij op.

Both are possible, but the word order changes because of verb-second.

Yes, both verbs are in the present tense:

• lichten
• duikt

Dutch often uses the present tense for:

• general statements
• near future
• sequences in a story
• planned or expected actions

So the sentence can naturally mean something like:

• We inform Tom; then he shows up.

Even if the meaning is future-like in English, Dutch often still uses the present tense.

The semicolon links two closely related main clauses:

• Wij lichten Tom in
• daarna duikt hij op

It shows a stronger connection than a full stop, but a clearer break than just a comma.

You could also write:

• Wij lichten Tom in. Daarna duikt hij op.
• Wij lichten Tom in, daarna duikt hij op.

The semicolon is a neat punctuation choice, but it does not change the grammar.

Yes. In everyday Dutch, we is very common.

So these both work:

• Wij lichten Tom in; daarna duikt hij op.
• We lichten Tom in; daarna duikt hij op.

Very broadly:

• we = more common in speech and informal writing
• wij = a bit more emphatic, careful, or formal in some contexts

At the start of a sentence, both are possible.

Because the subject is hij (he), so the verb must be conjugated for third person singular.

The infinitive is:

• duiken

But with hij, the present tense is:

• ik duik
• jij duikt
• hij duikt
• wij duiken

So:

• hij duikt op

The same kind of thing happens with lichten:

• wij lichten
• hij licht

A few parts may stand out to English speakers:

• wij contains the Dutch ij, which sounds different from English vowels.
• duikt contains ui, another very Dutch vowel sound.
• hij has the same ij sound as wij.
• In normal speech, we is often easier to pronounce than wij for beginners.

Also, separable verbs are pronounced as two parts in the sentence:

• lichten ... in
• duikt ... op

But when you say the infinitive, they are one word:

• inlichten
• opduiken

Not as a normal independent main clause.

If it is a main clause, Dutch needs verb-second:

• Daarna duikt hij op.

But in a subordinate clause, the verb goes to the end, and the separable verb comes back together in a different way:

• ..., omdat hij daarna opduikt. = ..., because he shows up afterwards.

So:

• main clause: Daarna duikt hij op.
• subordinate clause: ... dat hij daarna opduikt.

This difference is very important in Dutch word order.