A kérelmező vár.

A is the Hungarian definite article, so here it works like English the.

A useful detail:

• a is used before most consonant sounds
• az is used before vowel sounds

So:

• a kérelmező
• but az ember

Kérelmező is a noun meaning applicant.

It is built from the verb kérelmez (to apply, to request formally) plus -ő, a common ending that can form a person who does the action.

So very roughly:

• kérelmez = to apply / request
• kérelmező = applicant, requester

This -ó / -ő ending is common in Hungarian:

• tanul = study
• tanuló = student / learner

Because Hungarian does not need a separate word for is when the main verb already carries the meaning of the action.

Here, vár is the full verb waits / is waiting, so nothing else is needed:

• A kérelmező vár.

Hungarian only uses forms of to be when they are actually needed as the main verb, for example in sentences like:

• A kérelmező fáradt. = The applicant is tired.

But in your sentence, wait is the action, so vár does the whole job.

Vár is present tense, third person singular.

Depending on context, Hungarian present tense can match either:

• waits
• is waiting

So A kérelmező vár. can naturally correspond to either one in English. Hungarian often does not make the same simple-vs-progressive distinction that English does.

Hungarian verbs usually show the person and number by their form, so subject pronouns are often omitted unless needed for emphasis or contrast.

Here:

• vár = he/she/it waits or is waiting

Because the subject a kérelmező is already stated, there is no need for a separate pronoun.

In fact, adding a pronoun would usually sound unnecessary unless you wanted emphasis:

• A kérelmező vár. = neutral
• Ő vár. = He/She is waiting

A rough pronunciation guide:

• kérelmező ≈ KAY-rel-meh-zuh
• vár ≈ vaar

A few important sound notes:

• é is a long e-type sound
• ő is a long front rounded vowel, which English does not really have
• á is a long open vowel, longer than a
• Hungarian stress usually falls on the first syllable:
  • KÉ-rel-me-ző
  • VÁR

Also, Hungarian spelling is very regular, so the accents are important and should not be ignored.

The accents are part of the spelling and they matter.

In this sentence:

• é
• ő
• á

These are not optional marks. They usually show a different vowel quality and/or vowel length.

For example:

• a and á are different vowels
• o, ó, ö, and ő are all distinct

So you should learn kérelmező and vár with the accents included, not as extra decoration.

The sentence as given is the most neutral word order:

• A kérelmező vár.

Hungarian word order is flexible, but changes in order often change the emphasis or information structure rather than the basic meaning.

For example:

• A kérelmező vár. = neutral statement
• Vár a kérelmező. = possible in context, but the focus/emphasis feels different

So yes, the order can change, but learners should treat A kérelmező vár as the normal neutral version.

Not always. Vár can be used both:

• without an object: to wait
• with an object: to wait for someone/something

Examples:

• A kérelmező vár. = The applicant is waiting.
• A kérelmező a választ várja. = The applicant is waiting for the answer.

Notice something important in the second example:

• várja instead of vár

That is because Hungarian has different verb forms depending on whether the object is definite. This sentence does not show that contrast, but it is something you will meet very early in Hungarian.

Because this is the basic present-tense, third-person singular, indefinite form of the verb.

Very roughly:

• várok = I wait
• vársz = you wait
• vár = he/she waits

Since there is no definite direct object in this sentence, the indefinite conjugation is used.

So:

• A kérelmező vár. is grammatically simple: subject + present-tense verb

This is one reason Hungarian sentences can look very short compared with English.