استراحة القهوة بعد حلقة النقاش.

Because this is not really a full sentence with a verb; it is a noun phrase or label-like expression.

In Arabic, short expressions used for schedules, signs, captions, headlines, or event programs often leave out verbs. So استراحة القهوة بعد حلقة النقاش means something like:

• Coffee break after the discussion panel
• A coffee break after the discussion session

If you wanted a full sentence, you could say something like:

• تكون استراحةُ القهوةِ بعدَ حلقةِ النقاشِ = The coffee break is after the discussion panel
• تأتي استراحةُ القهوةِ بعدَ حلقةِ النقاشِ = The coffee break comes after the discussion panel

Literally, استراحة القهوة means the break of coffee or coffee’s break, but in natural English we say coffee break.

This is an iḍāfa construction, also called a construct phrase:

• استراحة = break / rest period
• القهوة = the coffee

Together:

• استراحة القهوة = coffee break

In Arabic, this structure often corresponds to X of Y or a compound noun in English.

This is how iḍāfa works.

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun can be definite, and if it is, the whole phrase becomes definite

So:

• استراحة القهوة = the coffee break
• literally: break of the coffee

Even though استراحة has no الـ, the whole phrase is definite because القهوة is definite.

This is a very common Arabic pattern:

• بابُ البيتِ = the door of the house
• مديرُ المدرسةِ = the principal of the school

Because بعد is followed by a noun phrase, and here that noun phrase is another iḍāfa:

• حلقة = circle / session / panel / episode
• النقاش = the discussion

So:

• حلقة النقاش = the discussion session / discussion panel

After بعد, Arabic commonly uses a noun in the genitive relationship within the iḍāfa phrase:

• بعدَ حلقةِ النقاشِ

In normal unvocalized writing, you just see:

• بعد حلقة النقاش

That is completely normal.

Literally, it means the circle of discussion.

The word حلقة originally means ring, circle, or something arranged in a circular form. From that, it also came to mean a session, panel, or group discussion, depending on context.

So حلقة النقاش can be understood as:

• discussion panel
• discussion session
• panel discussion

The exact English translation depends on context, but the Arabic phrase itself is very natural.

Yes.

Just like استراحة القهوة, حلقة النقاش is also an iḍāfa:

• حلقة = session / panel
• النقاش = the discussion

So the full expression contains two iḍāfa phrases:

1. استراحة القهوة
2. حلقة النقاش

This is very common in Arabic. You can think of the structure as:

• [coffee break] after [discussion panel]

A careful MSA pronunciation would be:

istirāḥat al-qahwa baʿda ḥalaqat an-niqāsh

If you include full case endings in very formal reading, it would be:

istirāḥatu l-qahwati baʿda ḥalaqati n-niqāshi

A few pronunciation notes:

• استراحة = istirāḥa / istirāḥat
  The final ة is pronounced as -t when the word is followed by another word in iḍāfa.
• القهوة = al-qahwa
• بعد = baʿda
• حلقة = ḥalaqa / ḥalaqat
• النقاش = an-niqāsh in connected pronunciation, because ن is a sun letter, so the l of الـ is assimilated

Because both words end in tāʾ marbūṭa: ة.

This letter is usually pronounced:

• as -a / -ah when the word stands alone
• as -t when the word is followed by another word in an iḍāfa or when case endings are pronounced

So:

• alone: استراحة → istirāḥa
• in iḍāfa: استراحة القهوة → istirāḥat al-qahwa

And:

• alone: حلقة → ḥalaqa
• in iḍāfa: حلقة النقاش → ḥalaqat an-niqāsh

This is an important pattern to notice.

بعد means after.

In this phrase, it introduces the time relationship:

• استراحة القهوة = coffee break
• بعد حلقة النقاش = after the discussion panel

So بعد tells you when the coffee break happens.

It is often followed by a noun or noun phrase:

• بعد الاجتماع = after the meeting
• بعد الدرس = after the lesson
• بعد انتهاء المحاضرة = after the lecture ends

Yes, but it changes the feel and usually the definiteness.

• استراحة القهوة = the coffee break
• استراحة قهوة = a coffee break or simply coffee break in a less definite sense

In many real contexts, both may appear, depending on whether the speaker means a specific known break or just the general type of break.

In formal event language, استراحة القهوة is very natural for the coffee break on a program or schedule.

There actually is definiteness, but Arabic shows it differently.

In English, you say the coffee break by putting the before the whole phrase.

In Arabic iḍāfa, definiteness is usually shown on the second noun, and that makes the whole phrase definite:

• استراحة القهوة = the coffee break

So Arabic does not need الـ on the first word here. The whole phrase is already definite because of القهوة.

In a fully vocalized formal version, it would typically be:

استراحةُ القهوةِ بعدَ حلقةِ النقاشِ

More precisely in connected formal grammar:

• استراحةُ = nominative, if this phrase is acting as the subject or heading of an implied sentence
• القهوةِ = genitive, because it is the second term of an iḍāfa
• بعدَ = usually منصوب in form here as a ظرف
• حلقةِ = genitive after بعد in this construction
• النقاشِ = genitive as second term of iḍāfa

In ordinary modern writing, these short vowels are usually omitted, so learners normally read:

استراحة القهوة بعد حلقة النقاش

Yes, very natural.

It sounds like something you would see in:

• a conference schedule
• an event program
• a seminar agenda
• a workshop outline

It is concise and idiomatic. Arabic often uses short nominal expressions like this in formal written contexts.