Η γιατρός δεν είναι διαθέσιμη τώρα, αλλά θα είναι μετά τις τρεις.

In Modern Greek, γιατρός is very commonly used for both male and female doctors. The article shows the gender here:

• ο γιατρός = the (male) doctor
• η γιατρός = the (female) doctor

So in this sentence, η tells you the doctor is female.

You may sometimes hear other feminine forms in certain contexts, but η γιατρός is the standard, very common way to say the female doctor.

Because adjectives in Greek usually agree with the noun they describe in gender, number, and case.

Here:

• η γιατρός = feminine singular
• so the adjective is also feminine singular: διαθέσιμη = available

Compare:

• ο γιατρός είναι διαθέσιμος = the male doctor is available
• η γιατρός είναι διαθέσιμη = the female doctor is available

So even though γιατρός has the same basic form for a man or a woman, the adjective makes the gender very clear.

δεν is the normal word for not before a verb in Greek.

So:

• είναι = is
• δεν είναι = is not

Greek negation usually goes directly before the verb:

• Δεν ξέρω = I don’t know
• Δεν έρχεται = He/She isn’t coming
• Δεν είναι διαθέσιμη = She isn’t available

So this is just the standard Greek way to negate a verb.

Greek commonly forms the future with θα + a verb form.

Here:

• είναι = is
• θα είναι = will be

So:

• δεν είναι διαθέσιμη τώρα = she is not available now
• θα είναι μετά τις τρεις = she will be after three

A very useful pattern is:

• θα
  • present/non-past verb form = future meaning

Examples:

• θα έρθει = he/she will come
• θα μιλήσω = I will speak
• θα είναι = he/she/it will be

Because Greek, like English, often leaves out words that are already obvious from the context.

Full version:

• Η γιατρός δεν είναι διαθέσιμη τώρα, αλλά θα είναι διαθέσιμη μετά τις τρεις.

Natural shortened version:

• Η γιατρός δεν είναι διαθέσιμη τώρα, αλλά θα είναι μετά τις τρεις.

The adjective διαθέσιμη is understood in the second part, so it doesn’t need to be repeated.

English does the same thing:

• She isn’t available now, but she will be after three.

It means after three o’clock.

Literally:

• μετά = after
• τις τρεις = three

In time expressions, Greek often uses the article, so μετά τις τρεις is the normal way to say after three.

The idea of o’clock is understood, so Greek does not need to say ώρα here.

Because after μετά, Greek uses the accusative case, and in this kind of time expression the article is normally included.

So:

• μετά
  • accusative
• τις τρεις = the accusative form used here

This is a fixed and very common pattern for clock times:

• στις τρεις = at three
• μετά τις τρεις = after three
• πριν τις τρεις = before three

So even though English just says after three, Greek normally says after the three in form.

Because an understood feminine noun is behind the expression: ώρα / ώρες (hour / hours).

Greek time expressions often behave as if they include ώρες, which is feminine plural, so the number appears in the feminine form:

• μία = one
• δύο
• τρεις = three
• τέσσερις = four

That is why you get:

• στις τρεις = at three
• μετά τις τρεις = after three

rather than τρία, which is the neuter form.

Greek usually uses the definite article much more often than English does.

So:

• Η γιατρός = the doctor

In a full sentence, Greek normally wants the article here. English might sometimes omit it in special contexts, but Greek generally does not.

For example:

• Η γιατρός είναι εδώ. = The doctor is here.
• Ο δάσκαλος λείπει. = The teacher is absent.

So the article in Η γιατρός is completely normal Greek.

The sentence order is natural and standard, but Greek word order is often more flexible than English word order.

This sentence is:

• Η γιατρός = the doctor
• δεν είναι διαθέσιμη = is not available
• τώρα = now
• αλλά = but
• θα είναι = will be
• μετά τις τρεις = after three

So the structure is very straightforward. But Greek can sometimes move adverbs like τώρα for emphasis.

For example, you might also hear:

• Η γιατρός τώρα δεν είναι διαθέσιμη...

That said, the version you have is the most neutral and natural one for learners to use.

You would change the article and the adjective to masculine:

• Ο γιατρός δεν είναι διαθέσιμος τώρα, αλλά θα είναι μετά τις τρεις.

Changes:

• Η → Ο
• διαθέσιμη → διαθέσιμος

The noun γιατρός stays the same, but the article and adjective show masculine instead of feminine.