Mi hermana tiene otro hueco el viernes por la mañana para gestionar la solicitud de su beca.

Yes, literally hueco can mean hole, gap, or empty space. But in everyday Spanish, especially in Spain, tener un hueco is a very common way to say to have a free slot / some time available / an opening in your schedule.

So here otro hueco means another free slot in her timetable.

It is natural and idiomatic. Similar alternatives would be:

• un rato libre
• un espacio
• disponibilidad (more formal)

But un hueco is probably the most everyday-sounding option in this context.

Because otro normally goes directly before the noun without un.

So Spanish says:

• otro día
• otra vez
• otro hueco

not un otro día or un otro hueco.

This is a normal rule with otro.

Compare:

• otro hueco = another free slot
• el otro hueco = the other free slot

So otro and el otro are both possible, but they mean different things.

Because otro agrees with hueco, not with hermana.

In Spanish, adjectives and similar words agree with the noun they belong to. Here:

• mi hermana = feminine
• hueco = masculine

So the sentence has:

• mi hermana
• otro hueco

That is completely normal. The fact that the person is female does not affect the gender of hueco.

With days of the week, Spanish normally uses the definite article:

• el lunes
• el martes
• el viernes

So el viernes means on Friday.

This is one of the standard differences from English. Spanish usually does not need a separate word for on here.

A useful contrast:

• el viernes = on Friday / this Friday
• los viernes = on Fridays / every Friday

So in your sentence, el viernes refers to one specific Friday.

Because por la mañana is the usual way to say in the morning when talking about when something happens.

So:

• el viernes por la mañana = Friday morning / on Friday in the morning

By contrast, de la mañana is very often used after a clock time:

• a las 9 de la mañana
• a las 11 de la mañana

So a simple way to remember it is:

• por la mañana = time period
• de la mañana = often used with specific hours

Also, in Spain, por la mañana is much more standard than en la mañana.

It expresses purpose: what the free slot is for.

So:

• tiene otro hueco = she has another free slot
• para gestionar... = to deal with / in order to handle...

A very important pattern is:

• para + infinitive

This is used when the subject stays the same.

Here, your sister is the one who has the free slot, and she is also the one who will do the action of gestionar, so para gestionar is correct.

If the subject changed, Spanish would usually use:

• para que + subjunctive

For example:

• Mi hermana tiene otro hueco para que su padre gestione la solicitud.

In this kind of sentence, gestionar has a slightly administrative or bureaucratic feel. In Spain, it is very common for paperwork, applications, official procedures, and practical arrangements.

Depending on context, it can mean things like:

• to handle
• to process
• to sort out
• to deal with
• to take care of

So it is more specific than just hacer.

Related verbs:

• gestionar = handle/manage an administrative matter
• tramitar = process official paperwork, often even more bureaucratic
• solicitar = apply for / request

Here gestionar la solicitud suggests dealing with the application process or paperwork, not just casually looking at it.

Yes, su solicitud de beca would also be very natural, and many learners will probably see that structure often.

A few points:

• solicitud = application / request
• solicitud de beca is a very common set phrase = scholarship application
• su solicitud de beca = her scholarship application

The version in your sentence, la solicitud de su beca, is understandable and grammatical, but solicitud de beca is the more fixed expression in many contexts.

So these are both possible kinds of phrasing:

• gestionar su solicitud de beca
• gestionar la solicitud de su beca

The second one links the application to her scholarship, while the first one more directly presents it as her scholarship application.

Yes, technically su is ambiguous on its own. It can mean:

• his
• her
• your (formal)
• their

In this sentence, the natural interpretation is her, referring to mi hermana, because that is the person already being talked about.

Spanish often relies on context for this kind of thing. If the speaker wanted to make it completely explicit, they could say something like:

• la beca de mi hermana
• su beca, la de mi hermana

But in normal conversation, su is often enough.

Because tener un hueco is the natural way to talk about a person’s availability.

• Mi hermana tiene otro hueco = My sister has another opening/free slot.

By contrast:

• Hay otro hueco = There is another opening.

So hay talks about existence in general, while tiene says that this free slot belongs to her schedule.

That is why tiene is the right choice here.

Usually, yes.

Otro means another, so it normally suggests:

• there was already one before, or
• another option had already been mentioned in the conversation

So the sentence gives the feeling that this is an additional available time, not the first one being discussed.

If you wanted to say only that she has a free slot, with no idea of an additional one, you would say:

• Mi hermana tiene un hueco...

Yes. Spanish is fairly flexible with word order, especially with time expressions and purpose phrases.

For example, you could also say:

• Mi hermana tiene otro hueco para gestionar la solicitud de su beca el viernes por la mañana.

That is still grammatical. But the original version sounds very natural because it places the time information early:

• otro hueco el viernes por la mañana

That makes the schedule detail easy to process right away.

So the original order is natural, and a changed order would usually be about emphasis or style rather than basic grammar.