Si no puedo ir al examen de junio, tendré que esperar a la siguiente convocatoria.

Because this is a real or possible condition: the speaker is talking about something that might actually happen.

After si in this kind of sentence, Spanish normally uses the indicative, not the subjunctive:

• Si no puedo ir... = if I can’t go...
• Si tengo tiempo... = if I have time...

The subjunctive after si is generally not used in standard modern Spanish for this type of condition.

This is the normal Spanish pattern for a first conditional:

• Si + present indicative, + future
• Si no puedo ir..., tendré que esperar...

In English, we do something similar:

• If I can’t go, I’ll have to wait.

So Spanish does not usually say Si no podré ir... here. The si clause takes the present tense, and the result clause can take the future.

Tendré que means I will have to.

It is made of:

• tendré = future of tener
• que
• infinitive: esperar

So:

• tendré que esperar = I will have to wait

This structure, tener que + infinitive, is one of the most common ways to express obligation in Spanish.

Yes, literally it means go to the exam, but in context it usually implies go and sit the exam.

In Spain, this is very natural. Depending on context, people might also say:

• presentarse al examen = to sit / take the exam
• hacer el examen = to do the exam
• asistir al examen = to attend the exam

So ir al examen is idiomatic and understandable, especially when the focus is on whether you can physically attend it.

El examen de junio means the June exam or the exam session in June.

Here, de junio identifies which exam it is, not just when it happens.

Compare:

• el examen de junio = the June exam / the June exam session
• el examen en junio = the exam in June

In many academic contexts in Spain, de + month is very common to label exam sessions:

• examen de enero
• examen de junio
• convocatoria de septiembre

Because a + el contracts to al in Spanish.

So:

• a + el examen → al examen

This contraction is normally mandatory.

The only common exception is when el is part of a proper name, such as:

• a El Escorial

But here el examen is not a proper name, so al examen is correct.

In Spain, convocatoria is a very common academic/administrative word. In this sentence, it means something like:

• exam sitting
• exam session
• opportunity to take the exam
• official round

So la siguiente convocatoria means the next exam session/opportunity.

This is especially common in Spain when there are multiple official chances to take an exam during the academic year.

Yes, both are possible.

• la siguiente convocatoria = the following/next exam session
• la próxima convocatoria = the next/upcoming exam session

In this context, they are very close in meaning. Siguiente can sound a little more like the one that comes after this one, while próxima can sound a little more like the upcoming one. But in everyday use, the difference is often small.

Good question. For learners, the safest rule is:

• esperar algo = to wait for something
• esperar a alguien = to wait for someone

So many teachers and textbooks would prefer:

• esperar la siguiente convocatoria

With things or events, esperar often appears without a.

That said, some native speakers do say esperar a before certain nouns or time-related expressions in everyday language. So esperar a la siguiente convocatoria may be heard, but esperar la siguiente convocatoria is often the more standard textbook choice.

Yes. That would also be natural, but it changes the nuance slightly.

• ir al examen focuses on going/attending
• hacer el examen focuses on taking/doing the exam
• presentarme al examen focuses on sitting the exam in a more formal way

So all of these can work, depending on what you want to emphasize.

Yes, especially because of convocatoria in the academic sense. That use is very typical in Spain.

A speaker from another Spanish-speaking country would still probably understand it, but in some places they might choose a different expression, such as:

• la próxima fecha de examen
• la siguiente oportunidad
• el próximo turno
• la próxima sesión

So the sentence sounds very natural for Spanish from Spain, particularly in an academic context.