Mi hermana tiene sed después de hacer ejercicio.

In Spanish, thirst is usually expressed with tener + noun:

• tener sed = to be thirsty
• literally, to have thirst

This is a very common pattern in Spanish, where English uses to be but Spanish uses to have:

• tener hambre = to be hungry
• tener sueño = to be sleepy
• tener frío/calor = to be cold/hot

You can say sedienta for thirsty, but tener sed is much more common and natural in everyday speech.

In modern Spanish, the normal way to say my sister is simply:

• mi hermana

Spanish uses short possessive adjectives directly before the noun:

• mi = my
• tu = your
• su = his/her/your/their

So:

• mi hermano = my brother
• mi hermana = my sister

Using an article before mi in this structure is not standard modern Spanish.

Tiene is the third-person singular form of tener in the present tense.

Conjugation of tener:

• yo tengo
• tú tienes
• él/ella/usted tiene
• nosotros/as tenemos
• ustedes/ellos/ellas tienen

Since mi hermana = she / my sister, the correct form is:

• Mi hermana tiene...

In the expression tener sed, Spanish normally does not use an article.

So you say:

• Tengo sed
• Ella tiene sed
• Tenemos sed

Not:

• Tengo la sed ❌

This is just part of the fixed expression. Many common Spanish expressions work this way.

Después de means after.

In this sentence, it introduces what happened before the main action/state:

• después de hacer ejercicio = after exercising / after doing exercise

A useful rule:

• después de + noun
  • después de la clase = after class
• después de + infinitive
  • después de comer = after eating
  • después de estudiar = after studying

So here, because the next verb is in the infinitive (hacer), de is required.

After después de, Spanish normally uses the infinitive when the action is general or when no separate subject needs to be stated:

• después de comer
• después de trabajar
• después de hacer ejercicio

So después de hacer ejercicio is the normal structure.

Haciendo ejercicio is the gerund (exercising / doing exercise), and it would be used in different kinds of sentences, for example:

• Está haciendo ejercicio. = She is exercising.

But after después de, the infinitive is the usual choice.

Yes. Hacer ejercicio is very common and natural across Latin America.

Examples:

• Hago ejercicio todos los días. = I exercise every day.
• Después de hacer ejercicio, tengo hambre.

You may also hear:

• ejercitarse = to exercise

But hacer ejercicio is often the most everyday, widely used option.

Yes, tras hacer ejercicio is grammatically correct and means basically the same thing as después de hacer ejercicio.

However:

• después de is more common in everyday speech
• tras can sound a bit more formal or literary in some contexts

For most learners, después de is the safest and most useful choice.

This is the standard Spanish word order:

• Mi hermana = subject
• tiene = verb
• sed = complement
• después de hacer ejercicio = time expression

Spanish word order is fairly flexible, but this version sounds natural and neutral.

You could move the time phrase for emphasis:

• Después de hacer ejercicio, mi hermana tiene sed.

That is also correct.

Yes. In this sentence, it is naturally understood that my sister is the one who exercised.

Spanish often uses:

• después de + infinitive

without repeating the subject, when the subject is clear from context.

So:

• Mi hermana tiene sed después de hacer ejercicio.

naturally means:

• My sister is thirsty after exercising

If the subject were different, Spanish would usually make that clearer in some other way.

They are gendered forms of the noun:

• hermana = sister
• hermano = brother

Because the person is female, the sentence uses:

• mi hermana

This is part of a broader pattern in Spanish:

• amigo / amiga
• hijo / hija
• profesor / profesora

Después is pronounced approximately like des-PWES.

The written accent on é shows where the stress goes:

• desPUÉS

Without the accent mark, the stress rules would suggest a different pronunciation, so the accent is necessary.

A rough pronunciation guide for the whole phrase:

• después de hacer ejercicio
• des-PWES de ah-SER e-her-SEE-syo (very approximate, depending on accent)

In much of Latin America:

• c before i in ejercicio sounds like s
• j in ejercicio is a strong h-like sound

Yes, that is grammatically correct, but it is less common in everyday speech than tiene sed.

Compare:

• Mi hermana tiene sed... = the most natural everyday phrasing
• Mi hermana está sedienta... = understandable, but often sounds a bit more descriptive or literary

For normal conversation, tener sed is usually the better choice.