Kundeservice siger, at varen er udsolgt lige nu, men at den snart kommer på lager igen.

In Danish, kundeservice usually works like an uncountable or institutional noun, much like English customer service.

So:

• Kundeservice siger ... = Customer service says ...

You would not normally say en kundeservice here, just as you would not usually say a customer service in English when you mean the department or function.

It is being treated as a singular thing, which is why the verb is siger.

Siger is the present tense of at sige = to say.

So:

• Kundeservice siger = Customer service says

Danish present tense is often very simple in form. Many verbs take -r in the present:

• sige → siger
• komme → kommer
• være → er

Because there are two subordinate clauses, both depending on siger:

• at varen er udsolgt lige nu
• men at den snart kommer på lager igen

So the structure is basically:

• Customer service says [that X], but [that Y].

In English, the second that is often omitted:

• Customer service says that the item is sold out right now, but that it will soon be back in stock.

In Danish, repeating at is very normal and often sounds clearer.

Sometimes, especially in casual speech, people may leave it out if the meaning is still obvious. But in a sentence like this, keeping it is very natural and often preferred.

So this version is standard and clear:

• ..., men at den snart kommer på lager igen.

It helps show that the second part is still part of what customer service is saying.

Vare means item/product/goods item.
Varen means the item/the product.

Here, a specific item is being talked about, so Danish uses the definite form:

• en vare = an item
• varen = the item

Danish usually adds the definite article to the end of the noun instead of using a separate word like English the.

Because vare is a common gender noun, and the singular definite ending for common gender nouns is usually -en.

So:

• en vare = an item
• varen = the item

Compare:

• en bil → bilen
• en butik → butikken
• en vare → varen

Den refers back to varen.

Since vare is a common gender noun, the correct pronoun is den:

• varen → den

If the noun were neuter (an et-word), Danish would use det instead.

Examples:

• en vare → den
• et hus → det

So den snart kommer på lager igen means it will soon be back in stock.

Because Danish pronouns must match the grammatical gender of the noun they refer to.

English has one main inanimate pronoun, it, but Danish has two:

• den for common gender nouns
• det for neuter nouns

Since vare is a common gender noun (en vare), the sentence must use den.

Udsolgt means sold out.

In this sentence:

• varen er udsolgt = the item is sold out

It describes the status of the item. Grammatically, it behaves like an adjective/past-participle-like form after er.

You will often see it in shops and online stores:

• Udsolgt = Sold out

Because udsolgt here describes a state, not an action being performed by the item.

• er udsolgt = is sold out

This is similar to English. You say:

• The item is sold out not
• The item has sold out in this meaning

So Danish uses er + udsolgt to describe the current condition.

Lige nu means right now or at the moment.

So:

• varen er udsolgt lige nu = the item is sold out right now

It softens the message a little by emphasizing that the sold-out status is temporary, especially since the sentence then says it will come back into stock.

Literally, it means something like:

• comes into stock again

But in natural English, that is usually translated as:

• will be back in stock
• will come back into stock

The phrase på lager is an idiomatic expression meaning in stock / in inventory.

So:

• komme på lager = to come into stock
• på lager igen = back in stock / in stock again

It is simply the standard expression. You should learn it as a fixed phrase.

• på lager = in stock
• ikke på lager = not in stock / out of stock

Even though the preposition may not match what English uses, this is the normal Danish wording.

Examples:

• Den er på lager. = It is in stock.
• Den er ikke på lager. = It is not in stock.

Danish very often uses the present tense to talk about the future when there is a time word that makes the future meaning clear.

Here, snart = soon, so the future is already obvious:

• den snart kommer på lager igen = it will soon be back in stock

This is very common in Danish.

English can also do something similar sometimes:

• It arrives tomorrow

But English often prefers will in many cases, while Danish is more comfortable using the plain present tense.

Yes, that is possible.

• den kommer snart på lager igen
• den vil snart komme på lager igen

Both can refer to the future.

The version with just the present tense often sounds more neutral and natural in everyday Danish when a time expression like snart is already there. The version with vil can sometimes sound slightly more explicit, but it is not necessary.

Because after at, you are in a subordinate clause, and Danish subordinate clauses normally keep the subject before the finite verb unless something else is placed before them.

So:

• at varen er udsolgt not
• at er varen udsolgt

This is a useful contrast with main clauses in Danish, where the verb often comes in second position.

Compare:

• Varen er udsolgt. = main clause
• Kundeservice siger, at varen er udsolgt. = subordinate clause

In subordinate clauses, sentence adverbs and time adverbs often appear before the finite verb.

So:

• at den snart kommer på lager igen

This word order is very natural in Danish subordinate clauses.

If this were a main clause, the word order could look different depending on what comes first:

• Den kommer snart på lager igen.

That difference in word order between main clauses and subordinate clauses is something learners often need time to get used to.

Igen means again.

Here it shows that the product was in stock before, is currently sold out, and will return to stock:

• på lager igen = back in stock / in stock again

In natural English, back in stock is often the best translation, even though Danish literally says in stock again.

The commas mark the subordinate clauses introduced by at.

• Kundeservice siger, at varen er udsolgt lige nu, men at den snart kommer på lager igen.

Danish punctuation often uses commas to separate this kind of clause structure clearly. Even if comma conventions can vary a little depending on style and formal rules learned in school, the commas here are completely normal and helpful.

Not always. Vare is a flexible word. Depending on context, it can mean:

• item
• product
• goods
• article

In this sentence, if it is an online store or webshop context, the item or the product would both work well.

So the Danish word is broad, and the best English choice depends on context.