La agencia de alquiler de autos está abierta.

Use estar here because abierta describes a state or condition: the agency is currently open for business.

• está abierta = is open
• está cerrada = is closed

If you used es abierta, it would usually sound like you were describing a more permanent quality, and with a person it can mean open-minded or outgoing. For a business being open at the moment, estar is the normal choice.

Because abierta agrees with la agencia, which is a feminine singular noun.

• la agencia → feminine singular
• so the adjective must match: abierta

Compare:

• La agencia está abierta.
• El banco está abierto.
• Las tiendas están abiertas.

This kind of gender-and-number agreement is very common in Spanish.

Spanish usually uses definite articles more often than English does. Here, la agencia means the agency.

In a sentence like this, the article sounds natural and complete:

• La agencia de alquiler de autos está abierta.

Without la, the sentence would sound incomplete in most normal contexts unless you were speaking in a special style such as signs, headlines, or notes.

Literally, it is something like:

• agencia = agency
• de alquiler = of rental / for renting
• de autos = of cars

So the whole phrase means car rental agency.

Spanish often builds noun phrases with de, where English might use a noun as an adjective:

• car rental agency in English
• agencia de alquiler de autos in Spanish

This is very normal Spanish structure.

Because each de connects a different part of the phrase:

• agencia de alquiler = agency for rental
• alquiler de autos = rental of cars

So the structure is layered:

[agencia] + [de alquiler] + [de autos]

Spanish uses de very often to link nouns together. English tends to pack nouns together more directly, as in car rental agency.

Yes, in many parts of Latin America, renta is also very common.

So both can be natural depending on region:

• agencia de alquiler de autos
• agencia de renta de autos

In Latin America, you may also hear:

• alquiler de carros
• renta de carros
• alquiler de coches in some places, though coches is more associated with Spain

The exact word choice depends a lot on the country.

Yes. Different regions prefer different words for cars.

Common options:

• autos — widely understood; common in many places
• carros — very common in much of Latin America
• coches — very common in Spain, but also understood in many places

Since the sentence is aimed at Latin American Spanish, autos is a good neutral choice.

Historically, it is the past participle of abrir (to open), but in this sentence it functions like an adjective.

• abrir → abierto / abierta
• La agencia está abierta.

Spanish uses many past participles as adjectives:

• La puerta está cerrada.
• La tienda está abierta.
• El banco está cerrado.

So for learners, it is easiest to think of abierta here as an adjective meaning open.

The structure is:

[Subject] + [estar] + [adjective]

So:

• La agencia de alquiler de autos = subject
• está = verb
• abierta = adjective

This is a very common pattern in Spanish for describing states:

• La tienda está cerrada.
• El restaurante está lleno.
• La oficina está abierta.

Not usually in this exact sentence, because the subject is the thing being talked about: the car rental agency.

You could leave it out only if it was already very clear from context:

• Está abierta. = It’s open.

But if you are introducing the idea for the first time, Spanish normally includes the noun:

• La agencia de alquiler de autos está abierta.

The given sentence is correct and natural, but in everyday conversation people might also say simpler versions, depending on context:

• La agencia de autos está abierta.
• La rentadora de autos está abierta. in some regions
• La agencia de renta está abierta.
• El lugar de alquiler de autos está abierto. though this is less standard

Learners should treat La agencia de alquiler de autos está abierta as a clear, standard model.

Está is pronounced roughly eh-STA.

The written accent shows that the stress falls on the second syllable:

• esTÁ

The accent mark is important because esta without an accent is a different word:

• esta = this (feminine)
• está = is

So:

• esta agencia = this agency
• la agencia está abierta = the agency is open