بعد ساعة لدينا اجتماع آخر في الشركة.

لدينا is made of لدى + نا.

• نا = we / us
• لدى literally means something like at or with

So لدينا اجتماع is literally at us there is a meeting, which is how Arabic often expresses we have a meeting.

A useful comparison:

• لدينا = more formal/written
• عندنا = very common in everyday speech

In Modern Standard Arabic, لدينا is a very natural choice here.

Arabic does not usually use a separate verb meaning to have the way English does.

Instead, possession is often expressed with a phrase like:

• لديّ = I have
• لدينا = we have
• عنده = he has
• عندها = she has

So لدينا اجتماع آخر is the normal Arabic way to say we have another meeting.

Literally, بعد ساعة means after an hour. But in English, when talking about something that will happen from now, we often say in an hour instead of after an hour.

So:

• بعد ساعة = after an hour / in an hour

Both ideas are the same here. Arabic uses بعد very naturally in this kind of time expression.

Because the meaning is an hour, not the hour.

So:

• بعد ساعة = after an hour / in an hour
• بعد الساعة would mean after the hour, which is a different and less natural meaning here

In Arabic, a singular indefinite noun often gives the sense of a/an.

In fully vowelled MSA, ساعة is in the genitive here:

• بعدَ ساعةٍ

That is because بعد is followed by a noun in an iḍāfa-like structure, and the following noun is treated as genitive.

So if all case endings were written, this part would be:

• بعدَ ساعةٍ

In normal unvowelled writing, you usually just see بعد ساعة.

Because adjectives normally come after the noun in Arabic.

So:

• اجتماع آخر = another meeting
• literally: meeting other/another

This is the normal order in Arabic. English usually puts adjectives before the noun, but Arabic usually puts them after.

Arabic adjectives agree with the noun they describe in things like:

• gender
• number
• definiteness
• case

Here:

• اجتماع is masculine singular
• it is indefinite
• so the adjective is آخر

That gives:

• اجتماع آخر = another meeting

If the noun were feminine, you would use أخرى instead:

• شركة أخرى = another company

If the noun were definite, the adjective would also be definite:

• الاجتماع الآخر = the other meeting

Here it means another.

With an indefinite singular noun, آخر often has the sense of another:

• اجتماع آخر = another meeting

It can also mean other in some contexts, and learners sometimes confuse it with last. For last/final, Arabic often uses الأخير more clearly:

• الاجتماع الأخير = the last meeting

So in this sentence, آخر should be understood as another, not last.

Because the time expression بعد ساعة already makes the future meaning clear.

Arabic often does this when the time is obvious from context. A sentence can refer to the future without an explicit future marker if there is a phrase like:

• غدًا = tomorrow
• بعد قليل = soon
• بعد ساعة = in an hour

So بعد ساعة لدينا اجتماع آخر is perfectly natural.

If you wanted to make the future more explicit, you could say:

• سيكون لدينا اجتماع آخر بعد ساعة

But the original sentence is simpler and very natural.

The preposition في basically means in, but in English the most natural translation with workplaces is often at.

So:

• في الشركة can mean in the company
• but in natural English here, at the company is often better

Also, الشركة has ال because it refers to a specific company that the speaker and listener know about.

Compare:

• في الشركة = at/in the company
• في شركة = at/in a company

Starting with the time expression is very common in Arabic. It sets the scene first:

• بعد ساعة = in an hour
• then the main information follows

So the sentence is structured a bit like:

• In an hour, we have another meeting at the company.

Arabic word order is flexible, but putting the time phrase first is natural and helps frame the sentence clearly.

In fully vowelled MSA, it would be:

بعدَ ساعةٍ لدينا اجتماعٌ آخرُ في الشركةِ

A few notes:

• بعدَ ends in fatḥa
• ساعةٍ is genitive
• اجتماعٌ is nominative
• آخرُ agrees with اجتماعٌ
• الشركةِ is genitive after في

One interesting detail: آخر is commonly treated as a diptote in this use, so in full vocalization you get آخرُ, not آخرٌ.

In ordinary Arabic writing, these endings are usually not written, which is why you normally just see:

بعد ساعة لدينا اجتماع آخر في الشركة