Vi har en elaftale med elselskabet.

Because Danish normally writes compound nouns as one word.

• el = electricity
• aftale = agreement/contract

So elaftale means an electricity agreement/contract.

This is very common in Danish. English often uses two words where Danish uses one:

• electricity company → elselskab
• house key → husnøgle
• coffee cup → kaffekop

A good rule is: if English has a noun + noun combination, Danish will often make it one word.

Because the grammatical gender comes from the last part of the compound noun.

The main noun here is aftale, and aftale is a common gender noun, so it takes en:

• en aftale
• therefore en elaftale

In Danish compounds, the final element decides things like:

• gender
• plural ending
• definite form

So even though el is added in front, the word is still treated like aftale.

For the same reason: it is a compound noun.

• el = electricity
• selskab = company

So:

• et selskab = a company
• et elselskab = an electricity company
• elselskabet = the electricity company

Again, Danish joins these parts into one word.

Because Danish usually puts the definite article at the end of the noun instead of using a separate word before it.

So:

• et selskab = a company
• selskabet = the company

And with the compound:

• et elselskab = an electricity company
• elselskabet = the electricity company

The ending -et is the definite article for many neuter nouns.

English says the electricity company. Danish says electricity-company-the, written as elselskabet.

Because selskab is a neuter noun.

In Danish:

• common gender nouns often take -en in the definite singular
• neuter nouns often take -et in the definite singular

So:

• et selskab → selskabet
• et elselskab → elselskabet

Since the head noun is selskab, the whole compound behaves like a neuter noun.

Har is the present tense of at have = to have.

So:

• jeg har = I have
• du har = you have
• vi har = we have

In this sentence, har means have/possess in the sense of being in possession of a contract or agreement.

Danish uses have very much like English here:

• Vi har en elaftale = We have an electricity contract

This is the normal Danish word order for a main clause:

subject + verb + rest of sentence

So:

• Vi = subject
• har = verb
• en elaftale = object
• med elselskabet = prepositional phrase

This is the standard neutral order.

Danish main clauses usually put the finite verb in second position, and that is exactly what happens here:

1. Vi
2. har

Med means with.

Here it links the agreement to the other party involved:

• en elaftale med elselskabet = an electricity contract with the electricity company

So med elselskabet tells you who the agreement is with.

This is very similar to English:

• an agreement with the company
• en aftale med selskabet

Yes, but it is a bit less specific.

• en aftale = an agreement / arrangement / deal
• en elaftale = specifically an electricity contract/agreement

So Vi har en aftale med elselskabet is grammatically fine, but elaftale makes it clearer that this is the contract for electricity supply, not just any arrangement with the company.

In Danish compounds, the last element is usually the main word.

So in:

• elaftale, the main word is aftale
• elselskab, the main word is selskab

That final part tells you what kind of thing it is:

• an elaftale is a kind of aftale
• an elselskab is a kind of selskab

This is very useful because the last part controls:

• gender: en/et
• definite ending: -en/-et
• plural form

Here are the key forms:

For elaftale:

• en elaftale = an electricity contract
• elaftalen = the electricity contract
• elaftaler = electricity contracts
• elaftalerne = the electricity contracts

For elselskab:

• et elselskab = an electricity company
• elselskabet = the electricity company
• elselskaber = electricity companies
• elselskaberne = the electricity companies

Learning nouns in these sets is often very helpful.

Yes. El is a normal Danish word meaning electricity in many everyday compound nouns.

You will often see it in words like:

• elbil = electric car
• elregning = electricity bill
• elforbrug = electricity consumption
• elselskab = electricity company

So elaftale fits a very common pattern.

Yes, that is the idea.

Elselskabet means the electricity company, so it sounds like a specific company already known from the context.

Compare:

• Vi har en elaftale med et elselskab = We have an electricity contract with an electricity company
  → any one company, not specified
• Vi har en elaftale med elselskabet = We have an electricity contract with the electricity company
  → a specific company, known in the situation

So the definite form shows that the speaker has a particular company in mind.