La empresa quiere ascenderla.

It is ascender + la.

• ascender = the infinitive verb
• la = a feminine singular direct-object pronoun

So ascenderla means to promote her or to move her up in this context.

Because Spanish allows object pronouns to attach to an infinitive.

So these two are both possible:

• La empresa quiere ascenderla.
• La empresa la quiere ascender.

Both mean the same thing. In sentences with a conjugated verb + infinitive, the object pronoun can often go:

• before the conjugated verb, or
• attached to the infinitive

La refers to the person or thing being promoted. In this sentence, it most naturally means her.

It replaces a feminine singular noun, such as:

• a María
• a la gerente
• a la empleada

So La empresa quiere ascenderla could come from something like La empresa quiere ascender a María.

Because here the promoted person is the direct object of ascender.

In standard Spanish, direct-object pronouns are:

• lo for masculine singular
• la for feminine singular

So:

• ascenderlo = to promote him / it
• ascenderla = to promote her / it

You may hear le in some varieties of Spanish because of leísmo, but for Latin American Spanish, la is the expected form here.

The personal a is used with a full noun, not with a direct-object pronoun.

Compare:

• La empresa quiere ascender a María.
• La empresa quiere ascenderla.

In the first sentence, a María is a full noun phrase, so the personal a appears. In the second, la is already a pronoun, so no a is used.

Because querer + infinitive is the normal pattern for to want to do something.

So:

• quiere = wants
• ascenderla = to promote her

Together:

• quiere ascenderla = wants to promote her

This is very common in Spanish:

• Quiero comer = I want to eat
• Queremos salir = We want to go out
• La empresa quiere ascenderla = The company wants to promote her

Because the subject is la empresa, which is grammatically singular.

Even though a company is made up of many people, the noun empresa is singular, so the verb is singular too:

• La empresa quiere...
• not La empresa quieren...

This is similar to English The company wants...

No. La here is just the feminine article for empresa.

In Spanish, nouns have grammatical gender:

• el libro
• la mesa
• la empresa

That does not mean the company is female. It only means empresa is a grammatically feminine noun, so it takes:

• la
• feminine adjectives if needed

Example:

• La empresa es grande.

No. This is a useful vocabulary point.

Ascender can mean different things depending on context, including:

• to rise / go up
• to amount to
• to promote

In this sentence, because the object is a person being moved upward in rank, ascender means to promote.

So here it is closer to promote than to the literal English verb ascend.

You would normally use the person’s name with the personal a:

• La empresa quiere ascender a María.
• La empresa quiere ascender a Ana.

Then, if you want to replace that person with a pronoun, you use la:

• La empresa quiere ascenderla.

So the pronoun version and the full noun version connect like this:

• a María → la
• a Ana → la