A parkolási engedély holnap lép érvénybe.

A is the definite article, meaning the.

In A parkolási engedély holnap lép érvénybe, it shows we are talking about a specific parking permit, not just parking permits in general.

A few related points:

• a and az both mean the
• Hungarian uses a before most consonants
• az is used before vowels

So:

• a parkolási engedély = the parking permit
• az engedély = the permit

Parkolási means something like parking-related or of parking.

It comes from the verb parkol = to park.
The ending -ási / -ési often turns a verb into a noun-like or adjective-like form referring to the activity.

So:

• parkol = to park
• parkolás = parking
• parkolási = parking / related to parking

That is why:

• parkolási engedély = parking permit

This kind of form is very common in Hungarian:

• fizetési mód = payment method
• belépési díj = entrance fee
• várakozási idő = waiting time

Because parkolási engedély is the normal way to say parking permit: literally, a permit connected with the activity of parking.

Compare:

• parkolási = relating to parking as an activity
• parkoló usually means parking lot, parking area, or sometimes parking as a present participle-like form

So:

• parkolási engedély = parking permit
• parkoló engedély would sound unnatural in this meaning

This is a vocabulary pattern you often just have to learn as a fixed expression.

Lép érvénybe is a fixed expression meaning comes into effect or enters into force.

Literally:

• lép = steps
• érvénybe = into validity / into force

But you should learn lép érvénybe as a whole phrase, because its real meaning is idiomatic.

It is often used in formal or administrative language:

• A törvény januárban lép érvénybe. = The law comes into effect in January.
• Az új szabály holnap lép érvénybe. = The new rule comes into effect tomorrow.

The ending -be means into.

Here it shows movement into a new state:

• érvény = validity, force
• érvénybe = into validity / into force

So lép érvénybe literally suggests step into force.

This is a common Hungarian way of expressing a change of state. Compare:

• működésbe lép = goes into operation
• hatályba lép = comes into force
• életbe lép = comes into effect

So the -be is there because Hungarian treats this as entering a state.

Because Hungarian very often uses the present tense to talk about the future when there is a clear time expression.

Here, holnap already tells you the action is in the future:

• holnap = tomorrow
• lép = present tense form, but understood as future because of holnap

This is extremely common in Hungarian, just as English can sometimes say things like:

• The train leaves tomorrow.

So:

• Holnap lép érvénybe. = It comes into effect tomorrow.

Hungarian does have ways to express future, but in many everyday and formal sentences, the present tense plus a future time word is the normal choice.

Yes, that is possible.

Hungarian word order is flexible, and changing the order changes the emphasis or information structure more than the basic meaning.

Compare:

• A parkolási engedély holnap lép érvénybe.
  Neutral and straightforward: The parking permit comes into effect tomorrow.

• Holnap lép érvénybe a parkolási engedély.
  This puts more attention on holnap = tomorrow.

• A parkolási engedély lép érvénybe holnap.
  Possible in some contexts, but less neutral.

In the original sentence, the topic is A parkolási engedély, and the new information is what happens to it and when.

Because Hungarian usually does not need a separate future marker here.

English often says:

• will come into effect

Hungarian commonly says the equivalent of:

• comes into effect tomorrow

That is enough because holnap already marks future time.

Hungarian does have a future construction with fog:

• érvénybe fog lépni

But in this sentence it would usually sound more formal, more explicit, or sometimes less natural than the simple present:

• A parkolási engedély holnap lép érvénybe. = the most natural version here

No, it is not possessed here.

Parkolási engedély is just a noun phrase meaning parking permit.
It is not literally the permit of parking in the grammatical possessive sense.

So:

• parkolási engedély = parking permit
• a parkolási engedély = the parking permit

If it were possessed, you might see forms like:

• az engedélye = his/her/its permit
• a parkolási engedélyem = my parking permit

So the basic form engedély is correct because this is simply a compound-like expression, not a possessed noun.

Not exactly, though they are close.

• lép érvénybe = comes into effect
• érvényes lesz = will be valid

The difference is mostly one of viewpoint:

• lép érvénybe focuses on the moment something starts to apply
• érvényes lesz focuses on the resulting state of being valid

So:

• A parkolási engedély holnap lép érvénybe.
  = The parking permit comes into effect tomorrow.

• A parkolási engedély holnaptól érvényes lesz.
  = The parking permit will be valid from tomorrow.

Both can work, but lép érvénybe sounds especially natural in official or administrative language.

Yes, it sounds somewhat formal or administrative.

That is mainly because of the phrase lép érvénybe, which is common in official notices, regulations, laws, permits, contracts, and similar contexts.

You might see it in:

• parking notices
• municipal rules
• legal texts
• public administration messages

A more conversational version might be phrased differently depending on context, but the original sentence is perfectly natural and correct, especially in official language.