Esa chica tan tranquila será la nueva profesora de yoga.

Esa means that and agrees with chica, which is feminine singular.

Very roughly:

• esta chica = this girl
• esa chica = that girl
• aquella chica = that girl over there / that girl further away

In real Spanish, the choice is not only about physical distance. It can also depend on whether the person is already known in the conversation or how the speaker mentally places them.

Because chica is feminine singular, the words that describe or point to it must match it.

Here the agreement is:

• esa → feminine singular
• tranquila → feminine singular
• nueva → feminine singular
• profesora → feminine singular

Spanish uses this kind of agreement much more visibly than English.

Tan means so before an adjective or adverb.

So:

• tan tranquila = so calm
• muy tranquila = very calm

They are close, but not identical:

• muy just intensifies
• tan often adds a stronger, more expressive feeling

Also, tan is the form used in structures like tan... como.

Because in Spanish, descriptive adjectives usually come after the noun.

So the neutral order is:

• una chica tranquila
• esa chica tan tranquila

If you move the adjective before the noun, it often sounds more literary, emotional, or marked:

• esa tranquila chica

That is possible in some contexts, but it is not the most neutral everyday order here.

Será is the 3rd person singular simple future of ser.

So:

• yo seré
• tú serás
• él/ella será
• nosotros seremos
• vosotros seréis
• ellos serán

In this sentence, será most naturally means will be.

The accent mark is part of the correct spelling of the future form.

• sera would be incorrect
• será is correct

The accent shows the stress falls on the last syllable: se-RÁ.

Because the sentence identifies someone as a teacher, which is a role/profession.

Spanish normally uses ser for:

• identity
• profession
• classification
• definitions

So:

• Es profesora
• Será la nueva profesora

Estar would not work here with this meaning.

That is a very common question. After ser, professions often appear without an article when you are speaking generally:

• Es profesora = She is a teacher

But here we are not just naming a profession in general. We are identifying a specific role:

• Será la nueva profesora de yoga = She will be the new yoga teacher

Because it is a specific, identifiable position, la is natural and needed.

With nuevo/nueva, position can change the nuance.

• la nueva profesora = the new teacher (the one who is replacing or joining)
• la profesora nueva = more like the teacher who is new or the new/inexperienced teacher, depending on context

In this sentence, la nueva profesora is the normal way to say the new yoga teacher.

Because de + subject/activity is commonly used to show what someone teaches or specializes in.

So:

• profesora de yoga
• profesor de matemáticas
• clase de inglés

Here yoga is treated as the field or discipline in a general sense, so no article is used.

Yes, it can.

In Spanish, the simple future can sometimes express probability or guesswork:

• Será la nueva profesora de yoga = She is probably the new yoga teacher

So without context, the sentence could mean either:

• She will be the new yoga teacher or
• She is probably the new yoga teacher

Context usually makes it clear which meaning is intended.