Πρέπει να στείλω την αίτηση μέχρι την Κυριακή.

Πρέπει is the usual Greek way to express necessity: must, have to, need to.

A key difference from English is that πρέπει is usually impersonal. It does not really mean I must by itself; more literally, it is closer to it is necessary.

So:

• Πρέπει να στείλω... = I must send... / I have to send...
• literally: It is necessary that I send...

That is why πρέπει stays the same no matter who the person is:

• Πρέπει να στείλω = I must send
• Πρέπει να στείλεις = you must send
• Πρέπει να στείλει = he/she must send

The person changes in the verb after να, not in πρέπει.

In Modern Greek, να is very commonly used before a verb where English might use an infinitive such as to send.

English says:

• I must send

Greek cannot simply say a direct equivalent of must send with an infinitive, because Modern Greek does not use the old infinitive in normal speech. Instead, it uses:

• πρέπει να στείλω

So να introduces the verb clause after πρέπει.

A useful way to think of it is:

• πρέπει να... = must / have to...

You will see this pattern constantly:

• Θέλω να φύγω = I want to leave
• Μπορώ να έρθω = I can come
• Πρέπει να στείλω = I must send

This is a very common learner question.

Στέλνω is the basic dictionary form: I send / I am sending.

But after να, Greek often chooses between two different verb forms depending on the meaning:

• να στέλνω = imperfective, repeated/ongoing/habitual action
• να στείλω = perfective, one complete action

Here, sending the application is a single completed action, so Greek uses να στείλω.

Compare:

• Πρέπει να στείλω την αίτηση.
  = I need to send the application.
  one completed act

• Πρέπει να στέλνω email κάθε μέρα.
  = I have to send emails every day.
  repeated/habitual action

So στείλω is used because the sentence is about completing the act of sending once.

Στείλω is the 1st person singular form used after να for a perfective action.

In learner-friendly terms, it means:

• that I send
• or more naturally in English here: I send

You do not need to memorize all the technical labels right away, but you should know these practical points:

• it means I
• it is used after να
• it refers to a single complete action

So in this sentence:

• να στείλω = for me to send / that I send
• natural English: to send

Greek often drops subject pronouns when they are not needed, because the verb ending already shows the person.

Here, στείλω already tells you the subject is I.

So:

• Πρέπει να στείλω την αίτηση... = I must send the application...
• Εγώ πρέπει να στείλω την αίτηση... = I must send the application...
  with extra emphasis on I

Greek usually includes εγώ only if there is contrast or emphasis, for example:

• Εγώ πρέπει να τη στείλω, όχι εσύ.
  = I have to send it, not you.

So the sentence sounds natural without εγώ.

Because αίτηση is a specific direct object here: the application.

• η αίτηση = the application
  nominative
• την αίτηση = the application
  accusative

Since it is the object of στείλω (send what?), Greek uses the accusative form.

So:

• στέλνω την αίτηση = I send the application

If you said just αίτηση with no article, it would sound more like an application or a less specific reference, depending on context. In this sentence, the article makes it definite and natural.

Greek very often uses the definite article with days of the week and time expressions.

So:

• Κυριακή = Sunday
• την Κυριακή = on Sunday / by Sunday / this Sunday, depending on context

After μέχρι, the phrase μέχρι την Κυριακή means by Sunday or until Sunday.

This article is normal Greek usage. English often leaves out the in time expressions, but Greek often keeps it.

Compare:

• τη Δευτέρα = on Monday
• την Τρίτη = on Tuesday
• την Κυριακή = on Sunday

It can suggest either, but in this sentence the natural English meaning is usually by Sunday because it gives a deadline.

• μέχρι την Κυριακή = by Sunday / until Sunday

The exact English choice depends on context:

• for a deadline, English usually says by Sunday
• for a time span continuing up to that point, English may say until Sunday

In this sentence, because the action is send the application, the intended meaning is most likely:

• the application needs to be sent no later than Sunday

So by Sunday is the most natural interpretation.

Greek word order is more flexible than English, because case endings and verb forms help show the relationships.

The given order is very natural:

• Πρέπει να στείλω την αίτηση μέχρι την Κυριακή.

But Greek could move things around for emphasis, for example:

• Πρέπει μέχρι την Κυριακή να στείλω την αίτηση.
• Την αίτηση πρέπει να στείλω μέχρι την Κυριακή.

These are still understandable, but they may sound more marked or place emphasis on a different part of the sentence.

For a learner, the original version is a good neutral pattern to use: πρέπει + να + verb + object + time expression

In meaning, it gives the time limit for the action of sending.

So it answers the question:

• By when do I have to send the application?
• Μέχρι την Κυριακή.

It is functioning as a time expression for στείλω.

You can think of the sentence structure like this:

• Πρέπει = necessity
• να στείλω = the action
• την αίτηση = what is sent
• μέχρι την Κυριακή = the deadline for that action

Yes, depending on the nuance.

The current sentence is the most natural way to say that a single sending action must be completed by Sunday.

But different forms would change the meaning:

• Πρέπει να στέλνω την αίτηση...
  would suggest repeated or habitual sending, which does not fit well here

• Έπρεπε να στείλω την αίτηση μέχρι την Κυριακή.
  = I had to send the application by Sunday
  past necessity

• Θα πρέπει να στείλω την αίτηση μέχρι την Κυριακή.
  = I will have to send the application by Sunday / I’ll need to send it by Sunday

So the original sentence is specifically good for a present obligation about one complete action.