Abban az esetben, ha elutasítják a kérelmünket, ideiglenes parkolási engedélyt igénylünk.

Yes. Abban az esetben, ha is a more formal, more bureaucratic way to say if or in the event that.

• ha = if
• abban az esetben, ha = in the event that / in case / if

So this sentence could be shortened to:

• Ha elutasítják a kérelmünket, ideiglenes parkolási engedélyt igénylünk.

That would be simpler and more everyday. The full version sounds more official.

Because eset is a noun here, and Hungarian normally uses the article with it in this expression.

Breakdown:

• abban = in that
• az esetben = the case / the event

So literally it is something like in that case/event.

This is a fixed expression:

• abban az esetben = in that case / in that event
• ebben az esetben = in this case

Because abban az esetben, ha... is the standard expression when introducing a condition like if...

Very roughly:

• ebben az esetben often means in this case
• abban az esetben, ha... often means in the event that...

So here abban is part of the established formal conditional phrase.

In Hungarian, 3rd person plural is often used when the subject is unspecified, especially in official or impersonal language.

So:

• elutasítják a kérelmünket literally = they reject our application
• but in natural English this is often translated as our application is rejected

The implied subject is something like:

• the authorities
• the office
• the decision-makers

Hungarian often uses this kind of unspecified they instead of a passive.

Because the object is definite: a kérelmünket = our application.

Hungarian verbs often have two conjugations:

• indefinite
• definite

Here:

• elutasítanak = they reject something nonspecific
• elutasítják = they reject it / the specific thing

Since a kérelmünket is a specific, definite object, Hungarian uses the definite verb form elutasítják.

It has three parts:

• kérelem = application / request
• kérelmünk = our application / our request
• kérelmünket = our application / request as the direct object

So:

• -ünk = our
• -t / -et = accusative marker, showing it is the object

This kind of stacking is very normal in Hungarian.

Because in Hungarian, possessed nouns can still take an article.

So Hungarian says things like:

• a házam = my house
• a könyvünk = our book
• a kérelmünket = our application (as object)

This is normal and does not sound redundant in Hungarian.

Parkolási means parking in the sense of related to parking.

It comes from:

• parkolás = parking
• parkolási = parking-related / for parking

This -i ending is very common in Hungarian for making an adjective from a noun.

So:

• parkolási engedély = parking permit

Because in Hungarian noun phrases, the case ending usually goes on the main noun, not on the adjectives before it.

So:

• ideiglenes = temporary
• parkolási = parking
• engedélyt = permit
  • accusative

Together:

• ideiglenes parkolási engedélyt = a temporary parking permit as the object

This is the normal Hungarian pattern.

Because the object is indefinite here.

Compare:

• ideiglenes parkolási engedélyt igénylünk = we apply for a temporary parking permit
• az ideiglenes parkolási engedélyt igényeljük = we apply for the temporary parking permit

In the original sentence, the permit is not presented as a specific already-identified permit, so there is no article.

This also affects the verb form.

Because the object is indefinite.

Hungarian uses:

• igénylünk with an indefinite object
• igényeljük with a definite object

Here the object is:

• ideiglenes parkolási engedélyt = a temporary parking permit

Since it is indefinite, the verb is also indefinite:

• igénylünk

This is one of the most important grammar points in the sentence:

• elutasítják is definite because a kérelmünket is definite
• igénylünk is indefinite because ideiglenes parkolási engedélyt is indefinite

Because Hungarian usually does not need subject pronouns when the verb ending already shows the subject.

• igénylünk already means we apply / we request

So mi is unnecessary unless you want emphasis:

• Mi igénylünk... = We are the ones who apply...

Most of the time, Hungarian leaves the pronoun out.

Because Hungarian often uses the present tense for future meaning when the context makes the time clear.

So:

• ha elutasítják... igénylünk...

can naturally mean:

• if they reject..., we will apply...

This is very common in Hungarian, especially in conditional or planned situations.

Yes. Hungarian word order is flexible, though it affects emphasis.

The original sentence puts the condition first:

• Abban az esetben, ha elutasítják a kérelmünket, ideiglenes parkolási engedélyt igénylünk.

You could also say:

• Ideiglenes parkolási engedélyt igénylünk, ha elutasítják a kérelmünket.

The basic meaning stays the same, but the original version sounds especially formal and structured, which fits official language.

Because Hungarian normally separates subordinate clauses with a comma.

Here the ha clause is subordinate:

• ha elutasítják a kérelmünket

Then the main clause follows:

• ideiglenes parkolási engedélyt igénylünk

So the comma is standard Hungarian punctuation.